Bound current

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 36A / a / Solution

{c}

In macroscopic matter with free charge density $\rho$ and free current density $J$,
$$
\nabla\cdot D=\rho,
\quad
\nabla\cdot B=0,
\quad
\nabla\times E=-\partial_tB,
\quad
\nabla\times H=J+\partial_tD.
$$
The electric displacement $D$ and magnetic field strength $H$ encode the material response.

These are the <Maxwell equations> after separating free and bound material sources.

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 Incoming links: Maxwell equations in matter