Ecuațiile lui Maxwell

Forma microscopică[]

Nume	Forma diferenţială	Forma integrală
Legea lui Gauss	$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$	$\int\!\!\!\!\!\!\!\!\;\!\;\!\subset\;\!\;\!\!\;\!\!\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\;\!\!\supset \mathbf E\;\cdot\mathrm{d}\mathbf A = \frac{Q(V)}{\varepsilon_0}$
Legea lui Gauss pentru magnetism	$\nabla \cdot \mathbf{B} = 0$	$\int\!\!\!\!\!\!\!\!\;\!\;\!\subset\;\!\;\!\!\;\!\!\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\;\!\!\supset \mathbf B\;\cdot\mathrm{d}\mathbf A = 0$
Legea Faraday	$\nabla \times \mathbf{E} = -\frac {\partial \mathbf{B}}{\partial t}$	$\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \frac {\partial \Phi_{B,S}}{\partial t}$
Legea lui Ampère	$\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t}\$	${\displaystyle \oint_{\partial S} \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \mu_0 I_S + \mu_0 \varepsilon_0 \frac {\partial \Phi_{E,S}}{\partial t} }$

Nume	Forma diferenţială	Forma integrală
Legea lui Gauss	$\nabla\cdot\mathbf{D} = \rho_f$	$\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\;\cdot\mathrm{d}\mathbf A = Q_{f}(V)$
Legea lui Gauss pentru magnetism	$\nabla \cdot \mathbf{B} = 0$	$\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf B\;\cdot\mathrm{d}\mathbf A = 0$
Ecuaţia Maxwell–Faraday (a inducţiei)	$\nabla \times \mathbf{E} = -\frac {\partial \mathbf{B}}{\partial t}$	$\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \frac {\partial \Phi_{B,S}}{\partial t}$
Legea lui Ampère	$\nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t}$	${\displaystyle \oint_{\partial S} \mathbf{H} \cdot \mathrm{d}\mathbf{l} = I_{f,S} + \frac {\partial \Phi_{D,S}}{\partial t} }$