Difference between revisions of "Ampere's law"

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'''Ampere's Law''' is a law that simplifies the calculation of the [[magnetic field]] at a point due to one or many [[current]]-carrying wires. It has many similarities to [[Gauss's Law]], and can be stated as:
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'''Ampere's Law''', named for [[Andre-Marie Ampere]], relates electric [[current]] to [[magnetic field]]s, and is one of [[Maxwell's Equations]].  It is often used in the calculation of the [[magnetic field]] at a point due to one or many [[current]]-carrying wires. It is the magnetic analogue to [[Gauss's Law]], and can be stated in integral form as
  
: <math>\oint_S \vec{B} \cdot \mathrm{d}\vec{s}  
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: <math>\oint_C \vec{B} \cdot \mathrm{d}\vec{s}  
 
= \mu_0 I_{\mathrm{enc}}</math>
 
= \mu_0 I_{\mathrm{enc}}</math>
  
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where <math>\vec{B}</math> is magnetic field, ''C'' is a closed curve, <math>I_{\mathrm{enc}}</math> is current enclosed by ''C'', and <math>\mu_0</math> is the permeability of free space.
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In differential form, Ampere's Law is written
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:<math> \vec{\nabla}\times\vec{B}=\mu_0\vec{J}</math>
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where <math>\vec{J}</math> is current density.
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[[category:Physics]]
 
[[category:Electricity]]
 
[[category:Electricity]]

Revision as of 21:14, 23 September 2008

Ampere's Law, named for Andre-Marie Ampere, relates electric current to magnetic fields, and is one of Maxwell's Equations. It is often used in the calculation of the magnetic field at a point due to one or many current-carrying wires. It is the magnetic analogue to Gauss's Law, and can be stated in integral form as

where is magnetic field, C is a closed curve, is current enclosed by C, and is the permeability of free space.


In differential form, Ampere's Law is written

where is current density.