## Equations of Electrostatics and Magnetostatics

In the most general case of distributions of charges and currents, Maxwell's Laws are:
$\mathbf{\nabla} \cdot \mathbf{E}=\frac{\rho}{\epsilon}$

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

$\mathbf{\nabla} \times \mathbf{E}=- \mu \frac{\partial H}{\partial t}$

$\mathbf{\nabla} \times \mathbf{H}=- \epsilon \frac{\partial E}{\partial t}+ \mathbf{J}$

In the case of static fields,
$\mathbf{E}, \mathbf{H}$
are constant, so that
$\frac{\partial \mathbf{E}}{\partial t} =\frac{\partial \mathbf{H}}{\partial t}=0$

Hence
$\mathbf{\nabla} \cdot \mathbf{E}=\frac{\rho}{\epsilon}$

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

$\mathbf{\nabla} \times \mathbf{E}=0$

$\mathbf{\nabla} \times \mathbf{H}= \mathbf{J}$