Maxwell's equations in matter

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Maxwell's equations are complete as far as classical electrodynamics are concerned. However, they are inconvenient when electrically and magnetically polarizable materials are present due to bound charges and currents. They can be expressed in a form which only reflects free charges and currents. Recall

$\mathbf{D} = \epsilon_0\mathbf{E} + \mathbf{P}$ ,

$\mathbf{B} = \mu_0\mathbf{(H + M)}$ .

Then Maxwell's equations become (SI units)

$\boldsymbol\nabla \cdot \mathbf{D} = \rho_f$ ,

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

$\boldsymbol\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}} {\partial t}$ ,

$\boldsymbol\nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t}$ .

Linear, isotropic media

on to boundary conditions for D and H

Retrieved from "http://www.physics.thetangentbundle.net/wiki/Classical_electrodynamics/Maxwell%27s_equations_in_matter"

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