Subject :- Applied Physics 2.

Topic :- Laser.

Difficulty :- Medium.

Static field: If the value of the physical quantity describing the field does not vary with time the field is called time invariant or a static field. Both static electric and magnetic fields are used in the design of many devices. For example, a static electric field can accelerate an electro and a static magnetic field can deflect if. This scheme is employed in the design of an oscilloscope , ink jet printer etc.

Gaussian surface can be constructed for the magnetic field as shown in figure below

The gaussian surface, even those that cut through the bar magnet do not enclose net magnetic charge because every cut through the magnet gives a piece having both north and south pole. Therefore, magnetic form of gauss law is written as $\Phi_{B}=\oint \vec{B}.\vec{ds}=0 $

This means that the net flux of the magnetic field through any closed surface is zero. This is called the gauss’s law for magnetic field in integral form.

Using divergence theorem the magnetic gauss law can be written as $$\oint_S \vec{B}.\vec{ds}=\oint_S (\vec{\nabla}.\vec{B})dv=0\\ or\ \vec{\nabla}.\vec{B}=0$$

This is called the differential or point form of magnetic gauss law.