Maxwell's equations

(Redirected from Ampere's Law)

Maxwell's equations describe the propagation of light (electromagnetic waves) through a medium. Maxwell's equations in Gaussian units are:

Faraday's law:

$\nabla\times\mathbf{E}=-\frac{1}{c}\frac{\partial\mathbf{B}}{\partial t}$

Ampere's law:

$\nabla\times\mathbf{H}=\frac{1}{c}\frac{\partial\mathbf{D}}{\partial t} + \frac{4\pi}{c}\mathbf{J}$

Poisson equation:

$\nabla\cdot\mathbf{D}=4\pi \rho$

Absence of magnetic monopoles:

$\nabla\cdot\mathbf{B}=0$

The Lorentz force:

$\mathbf{F}=q\left(\mathbf{E}+\frac{\mathbf{v}}{c}\times\mathbf{B}\right)$

Other relations:

$\mathbf{D}=\epsilon\mathbf{E};\qquad\mathbf{B}=\mu\mathbf{H}$

In a plasma, $\mu\approx 1,\,\epsilon\approx 1$

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