Conservapedia - User contributions [en]

Maxwell's Equations

2007-06-11T14:59:03Z

CScience: OK, Faraday only gets credit for generators. Motors were based on experiments by Oersted.

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[C. A. Coulomb|Charles-Augustin Coulomb]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms through the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating an electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>
===Absence of Magnetic Monopoles===
The second of the equations is just like the first, but for the magnetic field. The divergence of B must be the spatial density of magnetic monopoles. Since they have never been observed (though various Grand Unified Theories might allow for them), the value is zero.

This wasn't formulated initially in terms of monopoles, but was actually a statement that magnetic "lines of force" (the lines that intuitively describe the field) never end. They just circulate around various conductors carrying electric current. In contrast to this, lines of the electric field can be thought to "begin" and "end" on charged particles.
===Faraday's Law===
The third equation contains the result of Faraday's experiments with "electromagnetic induction"—a changing magnetic field creates an electric field, and that electric field circulates around the area experiencing the change in total magnetic flux. (Remember that the curl operator measures the extent to which a vector field runs in circles.) We won't go into the details of his experiments, except to note that he discovered that moving a coil of wire (a loop to pick up a circulating electric field) through a magnetic field (for example, by putting it on a shaft and turning it) led to the invention of electric generators, and hence made a major contribution to the industrialization of the world. Not bad for a theoretician.

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T02:16:12Z

CScience: /* Faraday's Law */

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[C. A. Coulomb|Charles-Augustin Coulomb]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms through the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating an electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>
===Absence of Magnetic Monopoles===
The second of the equations is just like the first, but for the magnetic field. The divergence of B must be the spatial density of magnetic monopoles. Since they have never been observed (though various Grand Unified Theories might allow for them), the value is zero.

This wasn't formulated initially in terms of monopoles, but was actually a statement that magnetic "lines of force" (the lines that intuitively describe the field) never end. They just circulate around various conductors carrying electric current. In contrast to this, lines of the electric field can be thought to "begin" and "end" on charged particles.
===Faraday's Law===
The third equation contains the result of Faraday's experiments with "electromagnetic induction"—a changing magnetic field creates an electric field, and that electric field circulates around the area experiencing the change in total magnetic flux. (Remember that the curl operator measures the extent to which a vector field runs in circles.) We won't go into the details of his experiments, except to note that he discovered that moving a coil of wire (a loop to pick up a circulating electric field) through a magnetic field (for example, by putting it on a shaft and turning it) led to the invention of electric motors and generators. Not bad for a theoretician.

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T02:15:26Z

CScience: Give credit where credit is due.

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[C. A. Coulomb|Charles-Augustin Coulomb]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms through the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating an electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>
===Absence of Magnetic Monopoles===
The second of the equations is just like the first, but for the magnetic field. The divergence of B must be the spatial density of magnetic monopoles. Since they have never been observed (though various Grand Unified Theories might allow for them), the value is zero.

This wasn't formulated initially in terms of monopoles, but was actually a statement that magnetic "lines of force" (the lines that intuitively describe the field) never end. They just circulate around various conductors carrying electric current. In contrast to this, lines of the electric field can be thought to "begin" and "end" on charged particles.
===Faraday's Law===
The third equation contains the result of Faraday's experiments with "electromagnetic induction"—a changing magnetic field creates an electric field, and that electric field circulates around the area experiencing the change in total magnetic flux. (Remember that the curl operator measures the extent to which a vector field runs in circles.) We won't go into the details of his experiments, except to note that he discovered that moving a coil of wire (a loop to pick up a circulating electric field) through a magnetic field (for example, by putting it on a shaft and turning it) led to the invention of the electric generator. Not bad for a theoretician.

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T02:04:48Z

CScience: Describe equation #3

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms through the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating an electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>
===Absence of Magnetic Monopoles===
The second of the equations is just like the first, but for the magnetic field. The divergence of B must be the spatial density of magnetic monopoles. Since they have never been observed (though various Grand Unified Theories might allow for them), the value is zero.

This wasn't formulated initially in terms of monopoles, but was actually a statement that magnetic "lines of force" (the lines that intuitively describe the field) never end. They just circulate around various conductors carrying electric current. In contrast to this, lines of the electric field can be thought to "begin" and "end" on charged particles.
===Faraday's Law===
The third equation contains the result of Faraday's experiments with "electromagnetic induction"—a changing magnetic field creates an electric field, and that electric field circulates around the area experiencing the change in total magnetic flux. (Remember that the curl operator measures the extent to which a vector field runs in circles.) We won't go into the details of his experiments, except to note that he discovered that moving a coil of wire (a loop to pick up a circulating electric field) through a magnetic field (for example, by putting it on a shaft and turning it) led to the invention of the electric generator. Not bad for a theoretician.

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T01:55:37Z

CScience: /* Integral Form */

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms through the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating an electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>
===Absence of Magnetic Monopoles===
The second of the equations is just like the first, but for the magnetic field. The divergence of B must be the spatial density of magnetic monopoles. Since they have never been observed (though various Grand Unified Theories might allow for them), the value is zero.

This wasn't formulated initially in terms of monopoles, but was actually a statement that magnetic "lines of force" (the lines that intuitively describe the field) never end. They just circulate around various conductors carrying electric current. In contrast to this, lines of the electric field can be thought to "begin" and "end" on charged particles.

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T01:53:42Z

CScience: Describe equation #2

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms thorough the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating an electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>
===Absence of Magnetic Monopoles===
The second of the equations is just like the first, but for the magnetic field. The divergence of B must be the spatial density of magnetic monopoles. Since they have never been observed (though various Grand Unified Theories might allow for them), the value is zero.

This wasn't formulated initially in terms of monopoles, but was actually a statement that magnetic "lines of force" (the lines that intuitively describe the field) never end. They just circulate around various conductors carrying electric current. In contrast to this, lines of the electric field can be thought to "begin" and "end" on charged particles.

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T01:40:34Z

CScience: /* Coulomb's Law */

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms thorough the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating an electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T01:39:20Z

CScience: /* Coulomb's Law */

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms thorough the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is repelling if they have like charges and attracting if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating and electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T01:38:14Z

CScience: /* Coulomb's Law */ Fill it in!

'''Maxwell's Equations''', formulated around 1861 by [[James Clerk Maxwell]] describe the interrelation between electric and magnetic fields.<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>They were a synthesis of what was known about electricity and magnetism, particularly building on the work of [[Michael Faraday]], [[Andre-Marie Ampere]], and others. These equations predicted the existence of [[Electromagnetic wave]]s, giving them properties that were recognized to be properties of light, leading to the (correct) realization that light is an electromagnetic wave. Other forms of electromagnetic waves, such as radio waves, were not known at the time, but were subsequently demonstrated by [[Heinrich Hertz]] in 1888. These equations are considered to be among the most elegant edifices of mathematical physics.

Maxwell's equations serve many purposes and take many forms. On the one hand, they are used in the solution of actual real-world problems of electromagnetic fields and radiation. On the other hand, they are the subject of admiration for their elegance. There are many T-shirts, typically obtainable on college campuses, sporting various forms of these equations.

What follows is a survey of the various forms that these equations take, beginning with the most utilitarian and progressing to the most elegant. Which form you prefer depends on your scientific outlook, and perhaps your taste in T-shirts. The various <math>\nabla \cdot \mathbf{E}</math> and <math>\nabla \times \mathbf{E}</math> symbols appearing in some of the equations are the [[divergence]] and [[curl]] operators, respectively.

They are usually formulated as four equations (but later we will see some particularly elegant versions with only two), and the equations are usually expressed in ''differential form'', that is, as [[Partial Differential Equations]] involving the divergence and curl operators. They can also be expressed with integrals. They are often expressed in terms of four vector fields: E, B, D, and H, though the simpler forms use only E and B.

{| class="wikitable" border="1" cellpadding="8" cellspacing="0"
! Name
! differential form
! integral form
|-
| Coulomb's law of electrostatics, or Gauss's Law:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|}

In these, '''E''' denotes the [[electric field]], '''B''' denotes the [[magnetic field]], '''D''' denotes the ''electric displacement field'', and '''H''' denotes the ''magnetic field strength'' or ''auxiliary field''. '''J''' denotes the free [[current density]], and <math>\rho</math> denotes the free [[electric charge density]].

==Integral Form==
Let's dispose of the integral form first. The integral forms can be seen to be equivalent to the differential forms thorough the use of the general [[Stoke%27s Theorem]]. The form known as ''Gauss's Theorem'' (k=3) takes care of the equations involving the divergence, and the form commonly known as just ''Stokes' Theorem'' (k=2) takes care of those involving the curl.

We will say nothing further about the equations in integral form. The differential versions are the "real" Maxwell equations.

==What the Four Equations mean==
===Coulomb's Law===
The first equation is just [[C. A. Coulomb|Coulomb]]'s law of electrostatics, manipulated very elegantly (as usual) by [[Michael Faraday|Faraday]] and [[Gauss]]. Coulomb's law simply says that the electric force between two charged particles acts in the direction of the line between them, is attracting if they have like charges and repelling if unlike, is proportional to the product of the charges, and is inversely proportional to the square of the distance between them:
:<math>F = \frac{q_1 q_2}{4 \pi \epsilon\ d^2}</math>

In this case, the constant defining the strength of the electric force is <math>4 \pi \epsilon</math> in the denominator. More about that presently.

In [[International_System_of_Units|SI units]] the charges are measured in [[International_System_of_Units#Coulomb|Coulombs]], the force in [[International_System_of_Units#Newton|Newtons]], the distance in [[International_System_of_Units#Meter|Meters]], and the value of <math>\epsilon</math> is <math>8.854 \times 10^{-12}</math> Coulombs2 per Newton meter2, or [[International_System_of_Units#Farad|Farads]] per meter.

Michael Faraday reformulated the electric and magnetic forces in terms of ''fields'' He said that what was really happening was that each charge was creating and electric field (called E) that acted on the other charge. The field created by the charge q1, as observed at distance d, is
:<math>E = \frac{q_1}{4 \pi \epsilon\ d^2}</math>
and points directly outward from that charge, in all directions. The force felt by charge q2 is
:<math>F = q_2 E</math>

Now consider a sphere of radius d with the charge at the center. If <math>\rho</math> is the charge density in Coulombs per cubic meter (Maxwell's equations are in terms of densities), the total charge in some volume is the integral, over that volume, of <math>\rho</math>.

So we have
:<math>q = \int_V \rho\, \mathrm{d}V</math>
Now the field at the surface of the sphere is
:<math>\frac{q_1}{4 \pi \epsilon\ d^2}</math>, or <math>\frac{1}{4 \pi \epsilon\ d^2} \int_V \rho\, \mathrm{d}V</math>
That field is directly outward, perpendicular to the sphere's surface, and is uniform over the surface. The integral of the field over the surface is <math>4 \pi d^2</math> times that (the surface area of the sphere is <math>4 \pi d^2</math>; this is why we have the pesky factor of <math>4 \pi</math> in various formulas; remember that d is the distance, and hence is the sphere's ''radius'', not its diameter), so
:<math>\int_V \frac{\rho}{\epsilon}\, \mathrm{d}V = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>
But, by Gauss's Theorem,
:<math>\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V</math>
So
:<math>\int_V \nabla \cdot \mathbf{E}\ \mathrm{d}V = \int_V \frac{\rho}{\epsilon}\, \mathrm{d}V</math>
Since this is true for any volume, we have
:<math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
Now D = <math>\epsilon\ E</math> in the straightforward case (more about that later), so
:<math>\nabla \cdot \mathbf{D} = \rho</math>

==Other Formulations==
In the language of [[Exterior Calculus]], Maxwell's equations can be rewritten much more compactly as:
:<math>\mathrm{d}\bold{F}=0</math>
:<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>
where '''d''' is [[exterior derivative]] operator, '''*''' is the [[Hodge star]] operator, and '''F''' is the Faraday tensor.

[[Category:Physics]]

== References ==
<references />

Maxwell's Equations

2007-06-11T00:31:20Z

CScience: Rework.

Maxwell's Equations

2007-06-11T00:12:31Z

CScience: Rework.

User:CScience

2007-06-10T19:53:50Z

CScience: add userboxes

{{userboxtop|CScience}}
{{user Christian1}}
{{user straightforwardbiblereading}}
{{user comp-3}}
{{user 6000YearOldEarth}}
{{user American}}
{{user pubschool}}
{{user CPA1Blk}}
{{user NoArbBlk}}
{{userboxbottom}}

Greetings. I'm a new (April 07) user, interested in science (and math) articles, from a creationist perspective where applicable.

I don't know how to do "userboxes", templates, or any of that fancy stuff.

I'm going to stay away from other topics, because of all the unpleasantness, blocking, banning, and complaining that I see. I recognize that running a site like this isn't easy, but I just don't want to get involved in those controversies. [[User:CScience|CScience]] 22:05, 24 May 2007 (EDT)

==June 8, 2007==

Unfortunately, I have decided not to attempt to edit anything related to Creation Science or related "controversial" subjects. I will stick to "hard science"—physics, chemistry, and mathematics. It had been my plan to work up to issues relating to Mach's principle and its implications for geocentrism, heliocentrism, and galaxy dynamics, but that won't happen.

It had not been my intention to write anything provocative relative to what seemed to be the norms of this web site. However, after looking around at various pages and talk pages, I can't figure out what is acceptable, what the policies actually are, and how those policies are applied. See, for example, the bickering on [[Talk:Geocentric_theory]], [[User_talk:CPAdmin1/Proposed_Block_Policy]], or many sysops' talk pages. The penalty for making a wrong judgment is severe—permanent banishment. It's not worth the risk. There is still plenty that I can do on non-controversial (I hope!) science, like try to explain [[Maxwell's Equations]] at the high school level. [[User:CScience|CScience]] 21:52, 8 June 2007 (EDT)

User:CScience

2007-06-09T01:52:56Z

CScience: Bailing out of controversy.

Greetings. I'm a new (April 07) user, interested in science (and math) articles, from a creationist perspective where applicable.

I don't know how to do "userboxes", templates, or any of that fancy stuff.

I'm going to stay away from other topics, because of all the unpleasantness, blocking, banning, and complaining that I see. I recognize that running a site like this isn't easy, but I just don't want to get involved in those controversies. [[User:CScience|CScience]] 22:05, 24 May 2007 (EDT)

==June 8, 2007==

Unfortunately, I have decided not to attempt to edit anything related to Creation Science or related "controversial" subjects. I will stick to "hard science"—physics, chemistry, and mathematics. It had been my plan to work up to issues relating to Mach's principle and its implications for geocentrism, heliocentrism, and galaxy dynamics, but that won't happen.

It had not been my intention to write anything provocative relative to what seemed to be the norms of this web site. However, after looking around at various pages and talk pages, I can't figure out what is acceptable, what the policies actually are, and how those policies are applied. See, for example, the bickering on [[Talk:Geocentric_theory]], [[User_talk:CPAdmin1/Proposed_Block_Policy]], or many sysops' talk pages. The penalty for making a wrong judgment is severe—permanent banishment. It's not worth the risk. There is still plenty that I can do on non-controversial (I hope!) science, like try to explain [[Maxwell's Equations]] at the high school level. [[User:CScience|CScience]] 21:52, 8 June 2007 (EDT)

Curl

2007-06-09T01:20:49Z

CScience: OK, try this.

The '''curl''' is a way of expressing a certain type of [[derivative]] of a [[vector field]]. It is defined for fields of 3-dimensional vectors on 3-dimensional space. The curl of a vector field is another vector field.

The curl is written as though it were the [[cross product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla"), with the given vector field, like this: <math>\nabla \times \vec V</math>. This is usually pronounced "curl V" or "del cross V".

In ordinary [[Cartesian coordinates]], the curl is calculated as:

:<math>\nabla \times \vec V = (\ \ \frac{\partial V_z}{\partial y} - \frac{\partial V_y}{\partial z},\ \ \ \ \frac{\partial V_x}{\partial z} - \frac{\partial V_z}{\partial x},\ \ \ \ \frac{\partial V_y}{\partial x} - \frac{\partial V_x}{\partial y}\ \ )</math>

or, using a somewhat fictitious notation like the [[determinant]] notation for cross product,
:<math>\nabla \times \vec V = \begin{vmatrix}
\hat x & \hat y & \hat z \\
\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\
V_x & V_y & V_z
\end{vmatrix}</math>
where <math>\hat x</math>, <math>\hat y</math>, and <math>\hat z</math> are the unit basis vectors.

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the cross product notation makes sense. This is also useful for remembering how to calculate a curl.

The curl is a true vector field operation—the result is independent of the coordinate system that is used. The proof of that, and its ramifications, are beyond the scope of this page.

The curl operation has an intrinsic "handedness" to it. Any physical phenomenon described by the curl operation (for example, magnetic fields), involves some kind of "right-hand rule".

The curl is an extremely important operation in physics, mathematics, and engineering. It is perhaps most famous for its appearance in [[Maxwell's Equations]].

Intuitively, the curl measures the degree to which the vector field rotates around a given point. If you were to measure the curl of the vector field of wind speed in the vicinity of a meteorological low pressure area, then, keeping in mind that the [[Coriolis force]] makes the wind move in a counterclockwise vortex in the Northern hemisphere, it would be a vector pointing upward. (The ''reason'' for the Coriolis force is not important here, we're just talking about the ''observation'' that the air moves in a counterclockwise vortex.) The way to see that the curl points upward is to visualize a giant right hand with the fingers curled counterclockwise—the thumb would point upward.

Vector fields with a curl of zero are called ''irrotational''.

[[Category:Mathematics]]
[[Category:Physics]]

Divergence

2007-06-09T00:57:06Z

CScience:

The '''divergence''' is a way of expressing a certain type of [[derivative]] of a [[vector field]]. It is typically defined for fields of 3-dimensional vectors on 3-dimensional space, but other dimensions are possible. The divergence of a vector field is a [[scalar field]], that is, just a number at each point in space.

The divergence is written as though it were the [[dot product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla"), with the given vector field, like this: <math>\nabla \cdot \vec V</math>. This is usually pronounced "div V" or "del dot V".

In ordinary [[Cartesian coordinates]], the divergence is calculated as:

:<math>\nabla \cdot \vec V = \frac{\partial V_x}{\partial x} + \frac{\partial V_y}{\partial y} + \frac{\partial V_z}{\partial z}</math>
or, using suitable notation,
:<math>\nabla \cdot \vec V = \sum_{i=1}^3 \frac{\partial V_i}{\partial x_i}</math>

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the dot product notation makes sense. This is also useful for remembering how to calculate a divergence.

The divergence is a true vector field operation—the result is independent of the coordinate system that is used. The proof of that, and its ramifications, are beyond the scope of this page.

The divergence is an extremely important operation in physics, mathematics, and engineering. It is perhaps most famous for its appearance in [[Maxwell's Equations]].

Intuitively, the divergence measures the degree to which the vector field is diverging from a given point. If you were to measure the divergence of the vector field of wind speed in the vicinity of a meteorological high pressure area, it would be positive, because the net motion of air is outward. If measured near a low pressure area, the divergence would be negative.

Vector fields with a divergence of zero are called ''solenoidal''.

[[Category:Mathematics]]
[[Category:Physics]]

Curl

2007-06-09T00:53:41Z

CScience: New page. Not finished!

The '''curl''' is a way of expressing a certain type of [[derivative]] of a [[vector field]]. It is defined for fields of 3-dimensional vectors on 3-dimensional space. The curl of a vector field is another vector field.

The curl is written as though it were the [[cross product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla"), with the given vector field, like this: <math>\nabla \times \vec V</math>. This is usually pronounced "curl V" or "del cross V".

In ordinary [[Cartesian coordinates]], the curl is calculated as:

:<math>\nabla \cdot \vec V = \frac{\partial V_x}{\partial x} + \frac{\partial V_y}{\partial y} + \frac{\partial V_z}{\partial z}</math>
or, using suitable notation,
:<math>\nabla \cdot \vec V = \sum_{i=1}^3 \frac{\partial V_i}{\partial x_i}</math>

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the cross product notation makes sense. This is also useful for remembering how to calculate a curl.

The curl is a true vector field operation—the result is independent of the coordinate system that is used. The proof of that, and its ramifications, are beyond the scope of this page.

The curl is an extremely important operation in physics, mathematics, and engineering. It is perhaps most famous for its appearance in [[Maxwell's Equations]].

Intuitively, the curl measures the degree to which the vector field rotates around a given point. If you were to measure the curl of the vector field of wind speed in the vicinity of a meteorological low pressure area, then, keeping in mind that the [[Coriolis force]] makes the wind move in a counterclockwise vortex in the Northern hemisphere, it would be a vector pointing upward. (The ''reason'' for the Coriolis force is not important here, we're just talking about the ''observation'' that the air moves in a counterclockwise vortex.) The way to see that the curl points upward is to visualize a giant right hand with the fingers curled counterclockwise—the thumb would point upward.

Vector fields with a curl of zero are called ''irrotational''.

[[Category:Mathematics]]
[[Category:Physics]]

Divergence

2007-06-09T00:41:10Z

CScience:

The '''divergence''' is a way of expressing a certain type of [[derivative]] of a [[vector field]]. It is typically a field of 3-dimensional vectors defined on 3-dimensional space, but other dimensions are possible. The divergence of a vector field is a [[scalar field]], that is, just a number at each point in space.

The divergence is written as though it were the [[dot product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla"), with the given vector field, like this: <math>\nabla \cdot \vec V</math>. This is usually pronounced "div V" or "del dot V".

In ordinary [[Cartesian coordinates]], the divergence is calculated as:

:<math>\nabla \cdot \vec V = \frac{\partial V_x}{\partial x} + \frac{\partial V_y}{\partial y} + \frac{\partial V_z}{\partial z}</math>
or, using suitable notation,
:<math>\nabla \cdot \vec V = \sum_{i=1}^3 \frac{\partial V_i}{\partial x_i}</math>

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the dot product notation makes sense. This is also useful for remembering how to calculate a divergence.

The divergence is a true vector field operation—the result is independent of the coordinate system that is used. The proof of that, and its ramifications, are beyond the scope of this page.

The divergence is an extremely important operation in physics, mathematics, and engineering. It is perhaps most famous for its appearance in [[Maxwell's Equations]].

Intuitively, the divergence measures the degree to which the vector field is diverging from a given point. If you were to measure the divergence of the vector field of wind speed in the vicinity of a meteorological high pressure area, it would be positive, because the net motion of air is outward. If measured near a low pressure area, the divergence would be negative.

[[Category:Mathematics]]
[[Category:Physics]]

Maxwell's Equations

2007-06-08T00:39:48Z

CScience: Apparently the double quote and the math stuff can split across a line. Don't need quote anyway.

Maxwell's Equations

2007-06-08T00:36:51Z

CScience: Tie in div and curl

Divergence

2007-06-08T00:34:54Z

CScience:

The '''divergence''' is a way of expressing a certain type of derivative of a [[vector field]]. It is typically a field of 3-dimensional vectors defined on 3-dimensional space, but other dimensions are possible. The divergence of a vector field is a [[scalar field]], that is, just a number at each point in space.

The divergence is written as though it were the [[dot product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla"), with the given vector field, like this: <math>\nabla \cdot \vec V</math>. This is usually pronounced "div V" or "del dot V".

In ordinary [[Cartesian coordinates]], the divergence is calculated as:

:<math>\nabla \cdot \vec V = \frac{\partial V_x}{\partial x} + \frac{\partial V_y}{\partial y} + \frac{\partial V_z}{\partial z}</math>
or, using suitable notation,
:<math>\nabla \cdot \vec V = \sum_{i=1}^3 \frac{\partial V_i}{\partial x_i}</math>

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the dot product notation makes sense.

The divergence is a true vector field operation—the result is independent of the coordinate system that is used. The divergence is an extremely important operation in physics, mathematics, and engineering. It is perhaps most famous for its appearance in [[Maxwell's Equations]].

Intuitively, the divergence measures the degree to which the vector field is diverging from a given point. If you were to measure the divergence of the vector field of wind speed in the vicinity of a meteorological high pressure area, it would be positive, because the net motion of air is outward. If measured near a low pressure area, the divergence would be negative.

[[Category:Mathematics]]
[[Category:Physics]]

Divergence

2007-06-08T00:29:11Z

CScience: New page! (One of many that will be needed to do Maxwell's equations correctly.)

The '''divergence''' is a way of expressing a certain type of derivative of a [[vector field]]. It is typically a field of 3-dimensional vectors defined on 3-dimensional space, but other dimensions are possible. The divergence of a vector field is a [[scalar field]], that is, just a number at each point in space.

The divergence is written as though it were the [[dot product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla") with the given vector field, like this: <math>\nabla \cdot \vec V</math>. This is usually pronounced "div V" or "del dot V".

In ordinary [[Cartesian coordinates]], the divergence is calculated as:

:<math>\nabla \cdot \vec V = \frac{\partial V_x}{\partial x} + \frac{\partial V_y}{\partial y} + \frac{\partial V_z}{\partial z}</math>
or, using suitable notation,
:<math>\nabla \cdot \vec V = \sum_{i=1}^3 \frac{\partial V_i}{\partial x_i}</math>

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the dot product notation makes sense.

The divergence is a true vector field operation—the result is independent of the coordinate system that is used. The divergence is an extremely important operation in physics, mathematics, and engineering. It is perhaps most famous for its appearance in [[Maxwell's Equations]].

Intuitively, the divergence measures the degree to which the vector field is diverging from a given point. If you were to measure the divergence of the vector field of wind speed in the vicinity of a meteorological high pressure area, it would be positive, because the net motion of air is outward. If measured near a low pressure area, the divergence would be negative.

[[Category:Mathematics]]
[[Category:Physics]]

Quantum mechanics

2007-06-07T18:29:46Z

CScience: Schrodinger's page says 1926 -- I'll take your word for it. 1927 was just from memory.

Quantum mechanics consists of the breakthrough in physics in the 1920s in understanding how particles behave inside atoms. Classical mechanics, as initially discovered by [[Isaac Newton]], cannot explain atomic behavior. [[Erwin Schrodinger]] is generally credited with the formulation of quantum mechanics, around 1926, with contributions from [[Werner Heisenberg]] and [[Niels Bohr]].

Classical mechanics would predict that an electron orbits a proton just as planets orbit the sun. Classical electromagnetism would predict that the orbiting electron would emit a time-varying electrical field just as a radio station does. But the electron would lose energy as it emits this radiation, and would orbit closer and closer to the proton, until it collapses into the proton! Such a model cannot be correct.

Quantum mechanics posits that an electron (or any other sub-atomic particle) behaves as both a wave and a particle. As a result of the wave nature of the electron, the position of the electron can never be precisely known. Whenever it is attempted to be measured, knowledge of the electron's velocity is lost. Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]].

Quantum mechanics forms the basis for our understanding of chemical reactions, as well as all computers and electronic devices today.

An important aspect of Quantum Mechanics is the predictions it makes about the radioactive decay of isotopes. Radioactive decay processes, controlled by the wave equations, are random events. A radioactive atom has a certain probability of decaying per unit time. As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time. The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second (9B) to quintillions of years (186W).

==Mathematics==

The mathematics of Quantum mechanics can be formulated in a number of ways: the "matrix mechanics" of Werner Heisenberg, the "path integrals" of [[Richard Feynman]], or the "wave mechanics" of Erwin Schrodinger. Wave mechanics is the most common formulation. It uses the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces.

==External Links==
For an excellent discussion of quantum mechanics, see:
http://www.chemistry.ohio-state.edu/betha/qm/

See also: [[Momentum (operator)]]

[[Category:Physics]]

Talk:Quantum mechanics

2007-06-07T18:25:32Z

CScience: First order kinetics

I have reinstated the change that had been made by Ssandoval, regarding the removal of "first order kinetics". It's true that he was an obvious vandal in other pages (yes, I looked around). It's also true that calling it an "idiotic implication" was excessive, and that his next "sentence" had no verb and contained a reference to a "negative amount" that I can't figure out. However, the chemical concept of "first order kinetics" isn't applicable here. Not idiotic, but wrong nonetheless. First order kinetics refers to a reaction rate ''per unit volume'' being proportional to the ''concentration'' of the reactants. In radioactivity the rate depends only on the amount of material. The exponential decay nevertheless follows.

Please look before reverting. [[User:CScience|CScience]] 14:25, 7 June 2007 (EDT)

Quantum mechanics

2007-06-07T18:15:20Z

CScience: Take out "kinetics"; see talk

Quantum mechanics consists of the breakthrough in physics in the 1920s in understanding how particles behave inside atoms. Classical mechanics, as initially discovered by [[Isaac Newton]], cannot explain atomic behavior. [[Erwin Schrodinger]] is generally credited with the formulation of quantum mechanics, around 1927, with contributions from [[Werner Heisenberg]] and [[Niels Bohr]].

Classical mechanics would predict that an electron orbits a proton just as planets orbit the sun. Classical electromagnetism would predict that the orbiting electron would emit a time-varying electrical field just as a radio station does. But the electron would lose energy as it emits this radiation, and would orbit closer and closer to the proton, until it collapses into the proton! Such a model cannot be correct.

Quantum mechanics posits that an electron (or any other sub-atomic particle) behaves as both a wave and a particle. As a result of the wave nature of the electron, the position of the electron can never be precisely known. Whenever it is attempted to be measured, knowledge of the electron's velocity is lost. Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]].

Quantum mechanics forms the basis for our understanding of chemical reactions, as well as all computers and electronic devices today.

An important aspect of Quantum Mechanics is the predictions it makes about the radioactive decay of isotopes. Radioactive decay processes, controlled by the wave equations, are random events. A radioactive atom has a certain probability of decaying per unit time. As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time. The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second (9B) to quintillions of years (186W).

==Mathematics==

The mathematics of Quantum mechanics can be formulated in a number of ways: the "matrix mechanics" of Werner Heisenberg, the "path integrals" of [[Richard Feynman]], or the "wave mechanics" of Erwin Schrodinger. Wave mechanics is the most common formulation. It uses the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces.

==External Links==
For an excellent discussion of quantum mechanics, see:
http://www.chemistry.ohio-state.edu/betha/qm/

See also: [[Momentum (operator)]]

[[Category:Physics]]

Gamma decay

2007-06-07T17:39:06Z

CScience:

'''Gamma decay''' is the process by which the [[nucleus]] of an [[atom]] emits a high energy [[photon]], that is, extremely short-wavelength [[Electromagnetic wave|electromagnetic radiation]].<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

It is one of three major types of [[radioactivity]] (the other two being [[alpha decay]] and [[beta decay]]).

Gamma decay is analogous to the emission of light (usually visible light) by decay in the orbits of the [[electron]]s surrounding the nucleus. In each case the energy states, and the wavelengths of the emitted radiation, are governed by the law of [[quantum mechanics]]. But while the electron orbits have relatively low energy, the nuclear states have much higher energy. For example, the sodium "D" spectral line has a wavelength of 0.6 microns and a corresponding quantum energy of about 2 electron volts, whereas a gamma ray emitted after cobalt-60 decay has a wavelength of about 1 picometer (10-12 meters) and a quantum energy of about 1 million electron volts.

Nuclei are not normally in excited states, so gamma radiation is typically incidental to alpha or beta decay—the alpha or beta decay leaves the nucleus in an excited state, and gamma decay happens soon afterwards.

Gamma radiation is the most penetrating of the three kinds. Gamma ray photons can travel through several centimeters of aluminum, for example.

==References==
<references/>

[[Category:Physics]]

Maxwell's Equations

2007-06-06T22:38:34Z

CScience: Might as well fix this now. I'll be back.

Maxwell's Equations

2007-06-06T22:35:53Z

CScience: Will revamp this page. The current form is one of the messiest known forms.

Gamma decay

2007-06-06T22:25:28Z

CScience: Now that I can see what I did ....

'''Gamma decay''' is the process by which the [[nucleus]] of an [[atom]] emits a high energy [[photon]], that is, extremely short-wavelength [[Electromagnetic wave|electromagnetic radiation]].<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

It is one of three major types of [[radioactivity]] (the other two being [[alpha decay]] and [[beta decay]]).

Gamma decay is analogous to the emission of light (usually visible light) by decay in the orbits of the [[electron]]s surrounding the nucleus. In each case the energy states, and the wavelengths of the emitted radiation, are governed by the law of [[quantum mechanics]]. But while the electron orbits have relatively low energy, the nuclear states have much higher energy. For example, the sodium "D" spectral line has a wavelength of 0.6 microns and a corresponding quantum energy of about 2 electron volts, whereas a gamma ray emitted after cobalt decay has a wavelength of about 1 picometer (10-12 meters) and a quantum energy of about 1 million electron volts.

Nuclei are not normally in excited states. Gamma radiation is typically incidental to alpha or beta decay—the alpha or beta decay leaves the nucleus in an excited state, and gamma decay happens soon afterwards.

Gamma radiation is the most penetrating of the three kinds. Gamma ray photons can travel through several centimeters of aluminum, for example.

==References==
<references/>

[[Category:Physics]]

Gamma decay

2007-06-06T22:24:01Z

CScience: My browser messed up.

'''Gamma decay''' is the process by which the [[nucleus]] of an [[atom]] emits a high energy [[photon]], that is, extremely short-wavelength [[electromagnetic radiation]].<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

It is one of three major types of [[radioactivity]] (the other two being [[alpha decay]] and [[beta decay]]).

Gamma decay is analogous to the emission of light (usually visible light) by decay in the orbits of the [[electron]]s surrounding the nucleus. In each case the energy states, and the wavelengths of the emitted radiation, are governed by the law of [[quantum mechanics]]. But while the electron orbits have relatively low energy, the nuclear states have much higher energy. For example, the sodium "D" spectral line has a wavelength of 0.6 microns and a corresponding quantum energy of about 2 electron volts, whereas a gamma ray emitted after cobalt decay has a wavelength of about 1 picometer (10-12 meters) and a quantum energy of about 1 million electron volts.

Nuclei are not normally in excited states. Gamma radiation is typically incidental to alpha or beta decay—the alpha or beta decay leaves the nucleus in an excited state, and gamma decay happens soon afterwards.

Gamma radiation is the most penetrating of the three kinds. Gamma ray photons can travel through several centimeters of aluminum, for example.

==References==
<references/>

[[Category:Physics]]

Gamma decay

2007-06-06T22:22:28Z

CScience: create page

Dmitri Mendeleev

2007-06-04T01:49:37Z

CScience: another link

'''Dmitri Mendeleev''' was born in 1834 in [[Siberia]]. He was the youngest of at least 14 children. In the late 1860s he began working on the [[Periodic Table of Elements|periodic table]] of the [[element]]s. By arranging all of the 63 elements then known by their [[Atomic mass|atomic weight]]s, he managed to organize them into groups possessing similar properties. When there was no element to fill in a space in the table, he envisioned a new element would one day be found and deduced its properties. Three of those elements were discovered during his lifetime: [[gallium]], [[scandium]], and [[germanium]].
{{DEFAULTSORT: Mendeleev, Dmitri}}
[[Category:Physicists]]
[[Category:Biographies]]

Dmitri Mendeleev

2007-06-04T01:47:57Z

CScience: fix link -- page had been moved

'''Dmitri Mendeleev''' was born in 1834 in [[Siberia]]. He was the youngest of at least 14 children. In the late 1860s he began working on the [[Periodic Table of Elements|periodic table]] of the [[element]]s. By arranging all of the 63 elements then known by their [[atomic weight]]s, he managed to organize them into groups possessing similar properties. When there was no element to fill in a space in the table, he envisioned a new element would one day be found and deduced its properties. Three of those elements were discovered during his lifetime: [[gallium]], [[scandium]], and [[germanium]].
{{DEFAULTSORT: Mendeleev, Dmitri}}
[[Category:Physicists]]
[[Category:Biographies]]

Alpha decay

2007-06-04T01:29:40Z

CScience: I will be careful. I will be careful. I will be careful.

'''Alpha decay''' is the process by which the [[nucleus]] of an [[atom]] disintegrates with the emission of a 4[[Helium|He]] nucleus, commonly called an "alpha particle".<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

It is one of three major types of [[radioactivity]] (the other two being [[beta decay]] and [[gamma decay]]).

Alpha decay can be thought of simply as the disintegration of an atomic nucleus because it is too big. Large nuclei have a greater mutual electrical repulsion from the protons that they contain. This is offset by the nuclear [[strong force]] that makes protons and neutrons stick together. As nuclei get larger, the repulsion overtakes the attraction, so a disintegrated nucleus has lower energy than a complete one, and the nucleus moves toward a state of lower energy. The phenomenon becomes barely noticeable for elements with [[atomic number]]s in the 60's, becomes important for atomic numbers in the 80's, and is the reason why the naturally occurring elements essentially stop with [[Uranium]] at atomic number 92. Synthetic elements with atomic numbers well above 100 typically have alpha half-lives of a few milliseconds.

One might wonder why the electrical repulsion of the protons is able to overcome the strong nuclear force, since the nuclear force is known to be about a million times stronger than the electrical force. The reason is that the electrical force is normally observed (for example, in ionization energies and in chemical bonds) ''at distances comparable to an atom's electron cloud''. The electrical force has an energy inversely proportional to distance, so that, when a charged particle is ''inside a nucleus'' its electrical energy is about 100,000 times greater, almost as strong as the nuclear force.

One might also wonder why such nuclei don't fall apart instantly. It happens that the nucleus has to pass through a temporary state of higher energy, which it can't do in classical mechanics, for the same reason water doesn't leak out of a glass by moving up over the edge. But under the rules of [[quantum mechanics]], an extremely tiny (on the atomic level) barrier can sometimes be breached. This is called [[quantum tunneling]]. It is a probabilistic phenomenon governed by the [[Heisenberg Uncertainty Principle]], so an unstable nucleus has a certain probability of disintegrating per second. This leads to the observed exponential decay and measured [[half-life]] of radioactive nuclei. Larger nuclei have a stronger tendency to disintegrate, so they can tunnel through the barrier more easily. This is why [[Uranium]] has a half-life of 4.5 billion years, whereas heavier artificial elements have half lives in milliseconds.

Heavy nuclei can actually disintegrate in many ways. They are most likely to disintegrate in ways that produce results ("daughter nuclei") that have the lowest energy. Helium (2 protons and 2 neutrons) has an extraordinarily low relative energy for reasons related to particle spin, so disintegration into a helium nucleus, plus whatever is left over, is by far the commonest form of decay. The "alpha particle" is, of course, a Helium nucleus. It was named an alpha particle long before it was discovered that this was a Helium nucleus, and even longer before it was known why this happens.

Other alpha-like decays, such as the emission of a [[Neon]] nucleus, have been observed, though they are incredibly rare.

[[Nuclear fission]], in which the two daughter nuclei are both very large, can be thought of as an extreme form of the same general phenomenon. It is normally quite rare (very long half-life), but it can be instantaneously provoked in certain "fissile" materials such as 235[[Uranium|U]] or 239[[Plutonium|Pu]] by exciting the nucleus with a [[neutron]].

==References==
<references/>

[[Category:Physics]]

Alpha decay

2007-06-04T01:28:21Z

CScience: Put the N>60 stuff in a better place, explain energy increase at nuclear distances.

'''Alpha decay''' is the process by which the [[nucleus]] of an [[atom]] disintegrates with the emission of a 4[[Helium|He]] nucleus, commonly called an "alpha particle".<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

It is one of three major types of [[radioactivity]] (the other two being [[beta decay]] and [[gamma decay]]).

Alpha decay can be thought of simply as the disintegration of an atomic nucleus because it is too big. Large nuclei have a greater mutual electrical repulsion from the protons that they contain. This is offset by the nuclear [[strong force]] that makes protons and neutrons stick together. As nuclei get larger, the repulsion overtakes the attraction, so a disintegrated nucleus has lower energy than a complete one, and the nucleus moves toward a state of lower energy. The phenomenon becomes barely noticeable for elements with [[atomic number]]s in the 60's, becomes important for atomic numbers in the 80's, and is the reason why the naturally occurring elements essentially stop with [[Uranium]] at atomic number 92. Synthetic elements with atomic numbers well above 100 typically have alpha half-lives of a few milliseconds.

One might wonder why the electrical repulsion of the protons is able to overcome the strong nuclear force, since the nuclear force is known to be about a million times stronger than the electrical force. The reason is that the electrical force is normally observed (for example, in ionization energies and in chemical bonds) ''at distances comparable to an atom's electron cloud''. The electrical force has an energy inversely proportional to distance, so that, when a charged particle is ''inside a nucleus'' its electrical energy is about 100,000 times greater, almost as strong as the nuclear force.

One might also wonder why such nuclei fall apart instantly. It happens that the nucleus has to pass through a temporary state of higher energy, which it can't do in classical mechanics, for the same reason water doesn't leak out of a glass by moving up over the edge. But under the rules of [[quantum mechanics]], an extremely tiny (on the atomic level) barrier can sometimes be breached. This is called [[quantum tunneling]]. It is a probabilistic phenomenon governed by the [[Heisenberg Uncertainty Principle]], so an unstable nucleus has a certain probability of disintegrating per second. This leads to the observed exponential decay and measured [[half-life]] of radioactive nuclei. Larger nuclei have a stronger tendency to disintegrate, so they can tunnel through the barrier more easily. This is why [[Uranium]] has a half-life of 4.5 billion years, whereas heavier artificial elements have half lives in milliseconds.

Heavy nuclei can actually disintegrate in many ways. They are most likely to disintegrate in ways that produce results ("daughter nuclei") that have the lowest energy. Helium (2 protons and 2 neutrons) has an extraordinarily low relative energy for reasons related to particle spin, so disintegration into a helium nucleus, plus whatever is left over, is by far the commonest form of decay. The "alpha particle" is, of course, a Helium nucleus. It was named an alpha particle long before it was discovered that this was a Helium nucleus, and even longer before it was known why this happens.

Other alpha-like decays, such as the emission of a [[Neon]] nucleus, have been observed, though they are incredibly rare.

[[Nuclear fission]], in which the two daughter nuclei are both very large, can be thought of as an extreme form of the same general phenomenon. It is normally quite rare (very long half-life), but it can be instantaneously provoked in certain "fissile" materials such as 235[[Uranium|U]] or 239[[Plutonium|Pu]] by exciting the nucleus with a [[neutron]].

==References==
<references/>

[[Category:Physics]]

Alpha decay

2007-05-31T23:45:31Z

CScience: Get a link right.

'''Alpha decay''' is the process by which the [[nucleus]] of an [[atom]] emits a package of two [[proton]]s and two [[neutron]]s, that is, an "alpha particle".<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

It is one of three major types of [[radioactivity]] (the other two being [[beta decay]] and [[gamma decay]]). Alpha decay is most common in atoms with a [[mass number]] greater than 60.

Alpha decay can be thought of simply as the disintegration of an atomic nucleus because it is too big. Large nuclei have a greater mutual electrical repulsion from the protons that they contain. This is offset by the nuclear [[strong force]] that makes protons and neutrons stick together. As nuclei get larger, the repulsion overtakes the attraction, so a disintegrated nucleus has lower energy than a complete one, and the nucleus moves toward a state of lower energy.

Why don't such nuclei fall apart instantly? It happens that the nucleus has to pass through a temporary state of higher energy, which it can't do in classical mechanics, for the same reason water doesn't leak out of a glass by moving up over the edge. But under the rules of [[quantum mechanics]], an extremely tiny (on the atomic level) barrier can sometimes be breached. This is called [[quantum tunneling]]. It is a probabilistic phenomenon governed by the [[Heisenberg Uncertainty Principle]], so an unstable nucleus has a certain probability of disintegrating per second. This leads to the observed exponential decay and measured [[half-life]] of radioactive nuclei. Larger nuclei have a stronger tendency to disintegrate, so they can tunnel through the barrier more easily. This is why [[Uranium]] has a half-life of 4.5 billion years, whereas heavier artificial elements have half lives in milliseconds.

Heavy nuclei can actually disintegrate in many ways. They are most likely to disintegrate in ways that produce results ("daughter nuclei") that have the lowest energy. Helium (2 protons and 2 neutrons) has an extraordinarily low relative energy for reasons related to particle spin, so disintegration into a helium nucleus, plus whatever is left over, is by far the commonest form of decay. The "alpha particle" is, of course, a Helium nucleus. (It was named an alpha particle long before it was discovered that this was a Helium nucleus, and even longer before it was known why this happens.)

Other alpha-like decays, such as the emission of a [[Neon]] nucleus, have been observed, though they are incredibly rare.

[[Nuclear fission]], in which the two result nuclei are both very large, can be thought of as another form of the same general phenomenon. It is normally quite rare (very long half-life), but it can be instantaneously provoked in "fissile" materials by exciting the nucleus with a [[neutron]].

==References==
<references/>

[[Category:Physics]]

Alpha decay

2007-05-31T23:39:43Z

CScience: Major expansion

'''Alpha decay''' is the process by which the [[nucleus]] of an [[atom]] emits a package of two [[proton]]s and two [[neutron]]s, that is, an "alpha particle".<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>

It is one of three major types of [[radioactivity]] (the other two being [[beta decay]] and [[gamma decay]]). Alpha decay is most common in atoms with a [[mass number]] greater than 60.

Alpha decay can be thought of simply as the disintegration of an atomic nucleus because it is too big. Large nuclei have a greater mutual electrical repulsion from the protons that they contain. This is offset by the nuclear [[strong force]] that makes protons and neutrons stick together. As nuclei get larger, the repulsion overtakes the attraction, so a disintegrated nucleus has lower energy than a complete one, and the nucleus moves toward a state of lower energy.

Why don't such nuclei fall apart instantly? It happens that the nucleus has to pass through a temporary state of higher energy, which it can't do in classical mechanics, for the same reason water doesn't leak out of a glass by moving up over the edge. But under the rules of [[quantum mechanics]], an extremely tiny (on the atomic level) barrier can sometimes be breached. This is called [[quantum tunneling]]. It is a probabilistic phenomenon governed by the [[Heisenberg uncertainty principle]], so an unstable nucleus has a certain probability of disintegrating per second. This leads to the observed exponential decay and measured [[half-life]] of radioactive nuclei. Larger nuclei have a stronger tendency to disintegrate, so they can tunnel through the barrier more easily. This is why [[Uranium]] has a half-life of 4.5 billion years, whereas heavier artificial elements have half lives in milliseconds.

Heavy nuclei can actually disintegrate in many ways. They are most likely to disintegrate in ways that produce results ("daughter nuclei") that have the lowest energy. Helium (2 protons and 2 neutrons) has an extraordinarily low relative energy for reasons related to particle spin, so disintegration into a helium nucleus, plus whatever is left over, is by far the commonest form of decay. The "alpha particle" is, of course, a Helium nucleus. (It was named an alpha particle long before it was discovered that this was a Helium nucleus, and even longer before it was known why this happens.)

Other alpha-like decays, such as the emission of a [[Neon]] nucleus, have been observed, though they are incredibly rare.

[[Nuclear fission]], in which the two result nuclei are both very large, can be thought of as another form of the same general phenomenon. It is normally quite rare (very long half-life), but it can be instantaneously provoked in "fissile" materials by exciting the nucleus with a [[neutron]].

==References==
<references/>

[[Category:Physics]]

Anion

2007-05-31T22:58:24Z

CScience: trivial

An '''anion''' (pronounced with 3 syllables, as in "'''an''' eye on") is a negatively charged [[ion]]<ref>Wile, Dr. Jay L. ''Exploring Creation With Chemistry''. Apologia Educational Ministries, Inc. 1998</ref>. It is the opposite of a [[cation]]. It is so named because, during [[electrolysis]], it migrates toward the [[anode]]. Anions are typically nonmetal ions. In a sodium chloride solution the Na+ ions are cations and the Cl- ions are anions.

==References==
<references/>

[[Category:Chemistry]]

Anion

2007-05-30T19:11:06Z

CScience: Pronunciation guide.

An '''anion''' (pronounced with 3 syllables, as in "'''an''' eye on")is a negatively charged [[ion]]<ref>Wile, Dr. Jay L. ''Exploring Creation With Chemistry''. Apologia Educational Ministries, Inc. 1998</ref>. It is the opposite of a [[cation]]. It is so named because, during [[electrolysis]], it migrates toward the [[anode]]. Anions are typically nonmetal ions. In a sodium chloride solution the Na+ ions are cations and the Cl- ions are anions.

==References==
<references/>

[[Category:Chemistry]]

Cation

2007-05-30T19:10:04Z

CScience: Improve pronunciation guide.

A '''cation''' (pronounced with a hard "t", as in "'''cat''' eye on") is a positively charged [[ion]]<ref>Wile, Dr. Jay L. ''Exploring Creation With Chemistry''. Apologia Educational Ministries, Inc. 1998</ref>. It is the opposite of an [[anion]]. It is so named because, during [[electrolysis]], it migrates toward the [[cathode]]. Cations are typically metal ions. In a sodium chloride solution the Na+ ions are cations and the Cl- ions are anions.

==References==
<references/>

[[Category:Chemistry]]

Category talk:Element

2007-05-30T17:03:22Z

CScience: typo

I agree. Please merge the "Element" and "Elements" categories together. [[User:Niandra|Niandra]][[User_talk:Niandra|talk]] 06:20, 14 May 2007 (EDT)

I also agree, but please use the title 'Element' (singular) if it is done. --[[User:Tomt|TomT]] 12:45, 18 May 2007 (EDT)

I agree, but tend to agree with the plural. TomT, why the singular? [[User:HeartOfGold|<big>HG</big>HeartOfGold]] [[User_talk:HeartOfGold|talk]] 13:41, 22 May 2007 (EDT)

While articles should be in the singular form, the standard wiki style is for categories to be in the plural form. Whatever the case, all categories should have the same count - either singular or plural. It would be much less work to make the standard plural than singular. --[[User:Mtur|Mtur]] 14:31, 22 May 2007 (EDT)

Whichever is done (I guess I agree with plural), there is an added wrinkle: there is a template "{Element|name=sodium, etc. etc}" in these pages. That template automatically puts it into the singular category "element". Many of these pages also have the explicit "[Category:Elements]" thing. They therefore appear in both categories. So, assuming that plural is decided upon, the template needs to be changed. Then all the explicit "[Category:Elements]" things can be taken out. In any case, someone with the authority to do so: '''please''' merge these. Then we can start filling out the periodic table in a way that would make Mendeleyev proud. (BTW, those are actually meant to be double brackets and curly braces, but I don't know how to quote them. Please bear with me.) [[User:CScience|CScience]] 19:20, 22 May 2007 (EDT)
:It appears to me that you've settled on it being the plural. That being the case, what do you need "someone in authority" for? The {{tl|element}} template is not currently protected, so any editor can change that, and anybody can change the individual articles (assuming they're not protected). My advice is, go ahead.
:Incidentally, to quote double brackets and the like, surround the relevant parts with <nowiki><nowiki></nowiki> codes, like this: <nowiki><nowiki>[[Category:elements]]</nowiki><nowiki></nowiki></nowiki>. The button on the editing toolbar of a red "banned" circle over a black "W" does this for you.
:[[User:Philip J. Rayment|Philip J. Rayment]] 09:58, 28 May 2007 (EDT)
::P.S. I guess this page should be moved to Category:Elements. I suggest that you make the other changes first, then I (or another sysop) can move this for you. [[User:Philip J. Rayment|Philip J. Rayment]] 10:04, 28 May 2007 (EDT)
:OK. Done. I'm off and running :-) The thing that was mystifying me (and making me think sysop intervention was required) was how inclusion of the "element" template automatically put the page in the category. I see it now. Thanks.
:I have taken out the "number of electrons" line (it's always the atomic number, and including it separately might confuse people into thinking there are circumstances under which it might be different.) And I have added the "normal state" line, for solid/liquid/gas. [[User:CScience|CScience]] 13:02, 30 May 2007 (EDT)

Category talk:Element

2007-05-30T17:02:13Z

CScience: Done!

I agree. Please merge the "Element" and "Elements" categories together. [[User:Niandra|Niandra]][[User_talk:Niandra|talk]] 06:20, 14 May 2007 (EDT)

I also agree, but please use the title 'Element' (singular) if it is done. --[[User:Tomt|TomT]] 12:45, 18 May 2007 (EDT)

I agree, but tend to agree with the plural. TomT, why the singular? [[User:HeartOfGold|<big>HG</big>HeartOfGold]] [[User_talk:HeartOfGold|talk]] 13:41, 22 May 2007 (EDT)

While articles should be in the singular form, the standard wiki style is for categories to be in the plural form. Whatever the case, all categories should have the same count - either singular or plural. It would be much less work to make the standard plural than singular. --[[User:Mtur|Mtur]] 14:31, 22 May 2007 (EDT)

Whichever is done (I guess I agree with plural), there is an added wrinkle: there is a template "{Element|name=sodium, etc. etc}" in these pages. That template automatically puts it into the singular category "element". Many of these pages also have the explicit "[Category:Elements]" thing. They therefore appear in both categories. So, assuming that plural is decided upon, the template needs to be changed. Then all the explicit "[Category:Elements]" things can be taken out. In any case, someone with the authority to do so: '''please''' merge these. Then we can start filling out the periodic table in a way that would make Mendeleyev proud. (BTW, those are actually meant to be double brackets and curly braces, but I don't know how to quote them. Please bear with me.) [[User:CScience|CScience]] 19:20, 22 May 2007 (EDT)
:It appears to me that you've settled on it being the plural. That being the case, what do you need "someone in authority" for? The {{tl|element}} template is not currently protected, so any editor can change that, and anybody can change the individual articles (assuming they're not protected). My advice is, go ahead.
:Incidentally, to quote double brackets and the like, surround the relevant parts with <nowiki><nowiki></nowiki> codes, like this: <nowiki><nowiki>[[Category:elements]]</nowiki><nowiki></nowiki></nowiki>. The button on the editing toolbar of a red "banned" circle over a black "W" does this for you.
:[[User:Philip J. Rayment|Philip J. Rayment]] 09:58, 28 May 2007 (EDT)
::P.S. I guess this page should be moved to Category:Elements. I suggest that you make the other changes first, then I (or another sysop) can move this for you. [[User:Philip J. Rayment|Philip J. Rayment]] 10:04, 28 May 2007 (EDT)
:OK. Done. I'm off and running :-) The thing that was mystifying me (and making me think sysop intervention was required) was how inclusion of the "element" template automatically put the page in the category. I see it now. Thanks.
:I have taken out the "number of electrons" line (it's always that atomic number, and including it separately might confuse people into thinking there are circumstances under which it might be different.) And I have added the "normal state" line, for solid/liquid/gas. [[User:CScience|CScience]] 13:02, 30 May 2007 (EDT)

Barium

2007-05-30T16:55:16Z

CScience: Category/template. Also, a "barium meal" doesn't sound appetizing. Let's say "ingestion" and not go into culinary details.

{{Element | name=Barium | symbol=Ba | anumber=56 | amass=137.3 amu | state=solid | class=Alkaline Earth | cstructure=Cubic | color=Silver | date=1808 | discname=[[Sir Humphrey Davy]] | origname=From the Greek ''barys'', meaning ''heavy''. | uses=Ingestion of barium is used in [[radiography]] to allow the alimentary canal to be viewed by [[x-ray]].| obtained=Barytine or Whiterite. }}

Helium

2007-05-30T16:47:08Z

CScience: category/template, note on alpha decay and source in gas wells

{{Element | name=Helium| symbol=He | anumber=2 | amass=4.0026 amu | state=gas | class=[[Noble Gas]]| cstructure=hexagonal close-packed | color=Colorless | date= August 18, 1868| discname= [[Pierre Janssen]]| origname= from [[Helios]] the [[Greek]] [[Sun]] [[Deity|god]] | uses=Unknown | obtained=. }}

'''Helium''' is the second element on the [[Periodic Table|periodic table of elements]]<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>. It is also the second most abundant element in the universe, after [[hydrogen]]. Helium is thought by some to have been created initially in [[The Big Bang]] creation event<ref> For a detailed account of this see: http://www.lbl.gov/abc/wallchart/chapters/10/0.html</ref>; however this is disputed <ref>see http://www.journals.uchicago.edu/ApJ/journal/issues/ApJL/v509n1/985623/985623.web.pdf</ref>, but what seems to be generally agreed is that subsequently helium has been created by by [[nuclear fusion]] in the center of stars <ref>A detailed account of this can be found at http://zebu.uoregon.edu/textbook/energygen.html</ref>. It is also the by-product of alpha-particle radioactivity. Radioactive decay of heavy elements deep inside the Earth sends Helium leaking into natural gas wells, from which it is obtained for commercial use.

Helium has an interesting history; during the nineteenth century, one of the things some scientists declared to be "impossible"<ref>[http://www.astrophysical.org/astrophysics.php Astrophysical.org]</ref> was the determination of the chemical makeup of the stars. Then spectroscopy was developed, and the composition of the stars became known in great detail. Helium, in particular, was discovered in the Sun (as an unknown element) ''before'' it was discovered on the Earth. It was, accordingly, named after ''helios,'' the Greek for the Sun.
It was first found in natural gas in 1905 at the [[University of Kansas]]. <ref>http://www.news.ku.edu/2000/00N/AprNews/Apr7/bailey.html</ref>.
==Notes and references==
<references/>

Lithium

2007-05-30T16:39:25Z

CScience: category/template

{{Element | name=Lithium | symbol=Li | anumber=3 | amass=6.941 amu | state=solid | class=Alkali metal | cstructure=Cubic or face-centered cubic | color=Silver | date=1817 | discname=[[Johann Arfvedson]] | origname=From the Greek word lithos (stone) | uses=Batteries, ceramics, lubricants | obtained=spodumene, lepidolite, pentalite}}
Lithium is an element<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>in the Alkali metals class of the periodic table. It is the lightest solid element--about half the density of water.

==References==
<references/>

Potassium

2007-05-30T16:37:42Z

CScience:

{{Element | name=Potassium | symbol=K | anumber=19 | amass=39.10 amu | state=solid | class=Alkali metal | cstructure=Body-Centered Cubic | color=Silver | date=1807 | discname=[[Davy, Sir Humphrey ]] | origname=From the Latin ''Kalium'' | uses=important biological role, and used in numerous industrial processes | obtained=sylvite, sylvinite, carnallite }}

'''Potassium''' is an element<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>in the Alkali metals class of the periodic table. It is so chemically active that it is never found free (in elemental form) in nature. In its elemental form, it reacts with water, forming potassium hydroxide and [[hydrogen]] gas, so violently that the hydrogen usually catches fire.

Its existence as "potash" or "vegetable alkali" (potassium carbonate), "caustic potash" (potassium hydroxide), etc., had long been known, but it was not isolated as an element until 1807, by Sir Humphrey Davy.

The radioactive decay of potassium provides a method of [[radiometric dating]] called [[potassium-argon dating]] that is used to calculate the ages of volcanic rocks.

==References==
<references/>

Sodium

2007-05-30T16:37:22Z

CScience: category/template

{{Element | name=Sodium | symbol=Na | anumber=11 | amass=22.99 amu | state=solid | class=Alkali metal | cstructure=Body-Centered Cubic | color=Silver | date=1807 | discname=[[Davy, Sir Humphrey ]] | origname=From the Latin ''Natrium'' | uses=important biological role, and used in numerous industrial processes | obtained=halite, trona }}
'''Sodium''' is an element<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>in the Alkali metals class of the periodic table. It is so chemically active that it is never found free (in elemental form) in nature. In its elemental form, it reacts violently with water, forming sodium hydroxide and [[hydrogen]] gas.

Its existence as salt (sodium chloride), "soda ash" or "mineral alkali" (sodium carbonate), lye or "caustic soda" (sodium hydroxide), etc., had long been known, but it was not isolated as an element until 1807, by Sir Humphrey Davy.

==References==
<references/>

Potassium

2007-05-30T16:36:26Z

CScience: category/template

Oxygen

2007-05-30T16:35:49Z

CScience: category/template, and word origin

{{Element | name=Oxygen | symbol=O | anumber=8 | amass=16.0 amu | state=gas | class=Non-metal | cstructure=Cubic | color=Colorless | date=1774 | discname=[[Joseph Priestly]] | origname=From the Greek words ''oxus'' (acid) and ''gennan'' (generate) | uses=Supports life | obtained=From liquid air}}

'''Oxygen''' is a [[chemical]] [[element]]<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref>. Oxygen's [[atomic mass]] is slightly under 16, since it also has 8 [[neutron]]s (a slight amount of mass is "lost" in the energy contained in the [[subatomic bond]]s).

The name "oxygen" means "acid maker": Many common acids -- nitric, sulfuric, phosphoric, etc. -- are just hydrogen nitrate, hydrogen sulfate, or hydrogen phosphate, where the nitrate, sulfate, and phosphate complexes involve oxygen.

Under [[normal condition]]s it is a colorless, odorless [[gas]] consisting of two oxygen [[atom|atoms]] which has the chemical formula O2. This means it is [[diatom]]ic. Approximately 20% of the [[atmosphere]] is made up of oxygen. Oxygen also forms a [[triatomic]] molecule called [[ozone]] (O3), which although unstable under normal conditions, is a very important ingredient in the upper [[atmosphere]].

Oxygen is highly reactive, and in many other elements and compounds undergo [[exothermic reaction]]s with it (they [[combustion|burn]] or [[oxidization|rust]]). If it were not for its continual replenishment as a waste product of plant [[photosynthesis]], the atmospheric oxygen would disappear, forming compounds with other chemicals at the earth's surface.

Many [[animal]]s depend upon oxygen as a highly efficient ingredient for breaking down [[food]] for [[energy]], due to its reactivity. Those that do not are called "[[anaerobic]]", meaning "without air", and include many important [[bacteria]].

==References==
<references/>

[[Category: hydrogen economy]]
[[Category:gases]]

Oxygen

2007-05-30T16:35:03Z

CScience: category/template, and word origin

Curium

2007-05-30T16:27:53Z

CScience: category/template

{{Element | name=Curium | symbol=Cm | anumber=96 | amass=247 amu | state=solid | class=Inner Transition metal | cstructure=Unknown | color=Unknown | date=1944 | discname=[[G. T. Seaborg]]| origname=Curium is named after [[Marie and Pierre Curie]]. | uses=Curium has no known uses. | obtained=Curium is Man-made. }}