Changes

'''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''', 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.

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.

==Integral Form==

==Integral Form==

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.

The integral forms can be seen to be equivalent to the differential forms through the use of the general [[Stoke's 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.

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

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 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.

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

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

==The Unification of Light with the Theory of Electromagnetism==

==The Unification of Light with the Theory of Electromagnetism==

It is possible, by means of experiments with electrical charges and currents, to find such a figure c² that has turned out to be the square of the velocity of propagation of electromagnetic effects. It could be demonstrated from static measurements of forces between two "unite" charges and between two "unit" currents that c ≈ 3.00 x 10 ⁸ms^-1. When Maxwell had performed this calculation with his equations for the first time, he could conclude that the system of electric and magnetic field will be propagated by this velocity and he realized the intriguing equivalence of this constant with the already experimentally determined speed of the light. Thus, he suggested that the light is the wave motion of the same medium that causes electric and magnetic phenomena. Electricity and magnetism had been unified by experimental works of [[Faraday]], [[Hans Christian Oersted|Ørsted]] and [[Ampère]]. After them, Maxwell carried out one of the greatest unifications in the physical sciences, the light ceased to be "something different" and have become electricity and magnetism in a new form - electromagnetic field propagated across the space.<ref>{{cite book |title=The Feynman Lectures on Physics, Volume 2 |author=Richard Phillips Feynman, Robert B. Leighton, Matthew Linzee Sands |publisher=Addison-Wesley |year=1966 |edition=2 |pages=18-9|url=http://books.google.com/books?ei=wJjyUe3-CsbMPYSegKgL&hl=sk&id=haXvAAAAMAAJ&dq=the+feynman+lectures+on+physics&q=electricity+and+magnetism+unified#search_anchor}}</ref>

It is possible, by means of experiments with electrical charges and currents, to find such a figure c² that has turned out to be the square of the velocity of propagation of electromagnetic effects. It could be demonstrated from static measurements of forces between two "unite" charges and between two "unit" currents that c ≈ 3.00 x 10 ⁸ms⁻¹. When Maxwell had performed this calculation with his equations for the first time, he could conclude that the system of electric and magnetic field will be propagated by this velocity and he realized the intriguing equivalence of this constant with the already experimentally determined speed of the light. Thus, he suggested that the light is the wave motion of the same medium that causes electric and magnetic phenomena. Electricity and magnetism had been unified by experimental works of [[Faraday]], [[Hans Christian Oersted|Ørsted]] and [[Ampère]]. After them, Maxwell carried out one of the greatest unifications in the physical sciences, the light ceased to be "something different" and have become electricity and magnetism in a new form - electromagnetic field propagated across the space.<ref>{{cite book |title=The Feynman Lectures on Physics, Volume 2 |author=Richard Phillips Feynman, Robert B. Leighton, Matthew Linzee Sands |publisher=Addison-Wesley |year=1966 |edition=2 |pages=18–9|url=http://books.google.com/books?ei=wJjyUe3-CsbMPYSegKgL&hl=sk&id=haXvAAAAMAAJ&dq=the+feynman+lectures+on+physics&q=electricity+and+magnetism+unified#search_anchor}}</ref>

==Other Formulations==

==Other Formulations==