Maxwells equations for the electric field {% E %} and magnetic field {% B %} in differential form.
{% \nabla \cdot E = \frac{1}{\epsilon_0} \rho %}
{% \nabla \cdot B = 0 %}
{% \nabla \times E = - \frac{\partial{B}}{\partial{t}} %}
{% \nabla \times B = \mu_0 J + \mu_0 \epsilon_0 \frac{\partial{E}}{\partial{t}} %}