electromagnetism
Biot-Savart Law
$$B(r) = \frac{\mu_0}{4\pi} \int \frac{I d\ell \times r'}{|r'|^3}$$
Maxwell's Equations
$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0},\ \nabla \cdot \mathbf{B} = 0,...$$
Ampere's Law
$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I$$
Gauss's Law
$$\oiint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$$