Subject :- Applied Physics 2.

Topic :- Laser.

Difficulty :- Medium.

Maxwell developed the concept of displacement current and accordingly modified the ampere’s law and knowing their importance put together the four equations. This package of four equations is known as Maxwell’s equations.

The static electric and magnetic fields are governed by the following postulates that form the foundation of electrostatics and magnetostatics.

1.Gauss law for electrostatics:

Differential form -------- $\vec{\nabla}.\vec{E}=\frac{\rho}{\epsilon_0}$

Integral form-------------------- $\int\vec{E}.\vec{ds}=\frac{Q}{\epsilon_0}$

2.Gauss law for magnetostatics:

Differential form---------- $\vec{\nabla}.\vec{B}=0$

Integral form -----------$\oint_S \vec{B}.\vec{ds}=0$

3.Faradays law of electrostatics

Differential form------------$\vec{\nabla}\times\vec{E}=0$

Integral form ---------------$\oint_C\vec{E}.\vec{dl}=0$

1. Ampere’s circuital law of magnetostatics

Differential form-------------$\vec{\nabla}\times\vec{B}=\mu_0\vec{J}$

Integral form----------------$\oint_C\vec{B}.\vec{dl}=\mu_0I$

In time varying Electric and magnetic fields, the Faraday’s law and Ampere’s circuital law are modified as follows---

1.Faraday’s law in time varying fields

Differential form---------$\vec{\nabla}\times\vec{E}=-\frac{\partial{B}}{\partial{t}}$

Integral form---------$\int\vec{E}.\vec{dl}=-\oint_S\frac{\partial{B}}{\partial{t}}.\vec{ds}$

2.Ampere’s law in time varying fields

Differential form ----------- $\vec{\nabla}\times\vec{H}=\vec{J}+\frac{\partial{D}}{\partial{t}}$

Integral form---------------------$\oint\vec{H}.\vec{dl}=\int\left(\vec{J}+\frac{\partial{D}}{\partial{t}}\right).\vec{ds}$