Maxwell’s equations

Electric Fields and Magnetic fields

\displaystyle \begin{aligned} \nabla \cdot \mathbf{E} &=\frac{\rho}{\varepsilon_{0}} \\ \nabla \cdot \mathbf{B} &=0 \\ \nabla \times \mathbf{E} &=-\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &=\mu_{0} \mathbf{j}+\frac{1}{c^{2}} \frac{\partial \mathbf{E}}{\partial t} \end{aligned}

1. Flux of electric field through surface is proportional to charge inside region bound by the surface.

2. Flux of magnetic field is zero.

3. Circulation of electric field around a loop is the negative rate of change of flux of the magnetic field out of surface bounded by the loop.

4. Circulation of magnetic field around a loop is the proportional to sum of rate of change of flux of electric field out of surface bounded by the loop and a quantity proportional to the flux of electric current out of the same surface. (one proportionality constant is the square of light velocity)

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