Electromagnetism

The unified force governing electrically charged particles.

Maxwell's Equations

These four partial differential equations form the foundation of classical electromagnetism, classical optics, and electric circuits.

NameEquation (Differential form)Meaning
Gauss's Law$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$Electric charge produces an electric field.
Gauss's Law for Magnetism$\nabla \cdot \mathbf{B} = 0$There are no magnetic monopoles.
Faraday's Law$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$A changing magnetic field produces an electric field.
Ampère's Law (with Maxwell)$\nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}\right)$Electric current and changing electric fields produce magnetic fields.