Give the explanation of Gauss’s law for magnetic field.

According to the figure let closed surface $S$. This surface kept in a magnetic field $\vec{B}$. The flux associated with this surface we have to determine. Imagine surface $S$ is divided into small area element. One such element is $\overrightarrow{\Delta S}$ and magnetic field associated with it is $\vec{B}$. The magnetic flux for this element is defined as,

$\Delta \phi_{\mathrm{B}}=\overrightarrow{\mathrm{B}} \cdot \overrightarrow{\Delta \mathrm{S}}$

Total flux $\phi_{\mathrm{B}}=\sum_{\text {all }} \Delta \phi_{\mathrm{B}}=\sum_{\text {all }} \overrightarrow{\mathrm{B}} \cdot \Delta \overrightarrow{\mathrm{S}}=0 \quad \ldots$ $(1)$

The number of lines leaving the surface is equal to the number of lines entering it. Hence, the net magnetic flux is zero.

In equation $(1)$ "all" stands for 'all area elements $\Delta \mathrm{S}$ '.

Gauss's law for magnetism is as below :

"The magnetic flux through any closed surface is zero".

Note : In equation ... $(1)$ if $\Delta \mathrm{S} \rightarrow 0$, then

$\phi=\int \overrightarrow{\mathrm{B}} \cdot \overrightarrow{d \mathrm{~S}}=0$

This equation is also a Gauss's law.