Maxwell's Equations

Maxwell's Equations of Electromagnetism:

Gauss' Law for Electrical Charge

$$\nabla ·\overrightarrow{\mathbf{E}}=4\pi \rho$$

Gauss' Law for Magnetism

$$\nabla ·\overrightarrow{\mathbf{B}}=0$$

Faraday's Law

$$\nabla \times \overrightarrow{\mathbf{E}}=-\frac{1}{c}\frac{\partial \overrightarrow{\mathbf{B}}}{\partial t}$$

Ampere's Law

$$\nabla \times \overrightarrow{\mathbf{B}}=\frac{1}{c}\left(4\pi \overrightarrow{\mathbf{J}}+\frac{\partial \overrightarrow{\mathbf{E}}}{\partial t}\right)$$