A nu se confunda cu relațiile lui Maxell din termodinamică.

Forma microscopică

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

Forma macroscopică

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