Equations

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    Maxwell's equations describe how electricity and magnetism relate to their sources and how they work.

Gauss's Law:   \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \frac{Q}{\varepsilon_0},  This Law states, put simply, that the electric flux through any closed surface is proportional to the enclosed electric charge.
                                  wikipedia.org


Gauss's Law for Magnetism:   \oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0  This law states that for each "volume space" there are just as many magnetic field lines going in as there are going out.
                                                                   wikipedia.org


Faraday's Law of Induction:     \Phi_B = \iint\limits_{\Sigma(t)} \mathbf{B}(\mathbf{r}, t) \cdot d \mathbf{A}\ ,   This law states that the induced electromotive force in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.                        wikipedia.org



Ampere's Law with Maxwell's correction:    \oint_C \mathbf{H} \cdot \mathrm{d}\boldsymbol{\ell} = \iint_S \left( \mathbf{J}_{\mathrm{f}} + \frac{\partial }{\partial t}\mathbf{D} \right) \cdot \mathrm{d} \mathbf{A} This law relates the magnetic field around a closed loop to the electic current passing in the loop.                                                                                    wikipedia.org