= Solution
<Maxwell's equations> in matter, with free charge and current densities, are
$$
\boxed{\nabla\cdot\mathbf D=\rho_{\rm free},\quad\nabla\cdot\mathbf B=0,\quad\nabla\times\mathbf E=-\frac{\partial\mathbf B}{\partial t},\quad\nabla\times\mathbf H=\mathbf J_{\rm free}+\frac{\partial\mathbf D}{\partial t}.}
$$
For vacuum, $\mathbf D=\epsilon_0\mathbf E$ and $\mathbf H=\mathbf B/\mu_0$, so the last equation is $\nabla\times\mathbf B=\mu_0\mathbf J+\mu_0\epsilon_0\,\partial\mathbf E/\partial t$.
Back to article page
