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.
| Name | Equation (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. |