Maxwell's Equations

Gauss’ Law

\[\nabla \cdot \vec{E} = \frac{1}{\epsilon_0} \rho\]

or the displacement version:

\[\nabla \cdot \vec{D} = \rho_f\]

(no name…no magnetic monopoles?)

\[\nabla \cdot \vec{B} = 0\]

Faraday’s Law \(\nabla \times \vec{E} = -\frac{\partial\vec{B}}{\partial t}\)

Ampere’s Law with Maxwell’s correction \(\nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial\vec{E}}{\partial t}\)

or the Auxillary/Displacement field version (it’s nicer looking, no?): \(\nabla \times \vec{H} = \vec{J} + \frac{\partial\vec{D}}{\partial t}\)