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Ampère's law (Redirected from Ampere's law)

In physics, Ampère's law is the magnetic equivalent of Gauss's law, discovered by André-Marie Ampère. It relates the circulating magnetic field in a closed loop to the electric current passing through the loop.

Contents

1 Original Ampère's law

2 Corrected Ampère's law: the Ampère-Maxwell equation

3 See also

4 References

5 External links

Original Ampère's law

$\oint_C \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\mathrm{enc}}$

where

$\mathbf{B}$ is the magnetic flux density,

$d\mathbf{l}$ is an infinitesimal element (differential) of the closed loop

C

I enc

is the current enclosed by the curve

C

μ 0

is the permeability of free space,

$\oint_C$ is the integral along the closed loop

C

Corrected Ampère's law: the Ampère-Maxwell equation

James Clerk Maxwell noticed a logical inconsistency when applying Ampère's law on charging capacitors, and thus concluded that this law had to be incomplete. To resolve the problem, he came up with the concept of displacement current and made a generalized version of Ampère's law which was incorporated into Maxwell's equations. The generalized formula is as follows:

$\oint_C \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\mathrm{enc}} + \mu_0 \epsilon_0 \frac{d \mathbf{\Phi_E}}{dt}$

where

$\mathbf{\Phi_E}$ is the flux of electric field through the surface.

This Ampère-Maxwell law can also be stated in differential form:

$\nabla\times\vec B = \mu_0 \vec J + \mu_0 \epsilon_0 \frac{\partial\vec E}{\partial t}$

where the second term arises from the displacement current; omitting it yields the differential form of the original Ampère's law.

References

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{{{Author|}}}{{|{{{3}}}}}}|show1| (2004)}}{{{{{Year|}}}}}}|show1|.}} {{|{{{3}}}}}}|show1|[{{{URL}}}}} Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.){{|{{{3}}}}}}|show1|]}}{{|{{{3}}}}}}|show1|, {{{Pages}}}}}{{|{{{3}}}}}}|Show1|, W. H. Freeman}}. {{{ID|}}}

External links

MISN-0-138 Ampere's Law (http://35.9.69.219/home/modules/pdf_modules/m138.pdf) (PDF file) by Kirby Morgan for Project PHYSNET (http://www.physnet.org).
MISN-0-145 The Ampere-Maxwell Equation; Displacement Current (http://35.9.69.219/home/modules/pdf_modules/m145.pdf) (PDF file) by J.S. Kovacs for Project PHYSNET.

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