James Clerk Maxwell

The life of James Clerk Maxwell - Unified Light and Electricity

Electric charge produces an electric field (Gauss's Law).

\[ \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \]

There are no magnetic monopoles (Gauss's Law for Magnetism).

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

A changing magnetic field produces an electric field (Faraday's Law).

\[ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \]

Electric currents and changing electric fields produce magnetic fields (Ampère-Maxwell Law).

\[ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \]