Physics equations/Maxwell's equations

under construction

Maxwell's equations integral form
$$\oint_S \vec{E} \cdot \mathrm{d}\vec{A} = \frac{1}{\epsilon_0} Q_{enc}$$

$$\oint_S \vec{B} \cdot \mathrm{d}\vec{A} = 0$$

$$\oint_C \vec{E} \cdot \mathrm{d}\vec{\ell} = -  \int_S \frac{\partial\vec{B}}{\partial t} \cdot \mathrm{d} \vec{A}$$

$$\oint_C \vec{B} \cdot \mathrm{d}\vec{\ell} = \mu \int_S \vec{J} \cdot \mathrm{d} \vec{A} +\frac{1}{c^2} \int_S \frac{\partial\vec{D}}{\partial t} \cdot \mathrm{d} \vec{A}$$