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

Explanation

According to the figure let closed surface S. This surface kept in a magnetic field `overset(to) (B)`. The flux associated with this surface we have to determine. Imagine surface S is divided into small area element. One such element is `overset(to) (Delta S)` and magnetic field associated with it is `overset(to) (B)`. The magnetic flux for this element is defined as, `Delta phi_(B) = overset(to) (B) . overset(to) (Delta S)`
Total flux `phi_(B) = sum_("all") Delta phi_(B) = sum_("all") overset(to) (B) . Delta overset(to) (S) = 0 .... (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 S`.
Gauss.s law for magnetism is as below :
"The magnetic flux through any closed surface is zero" .
Note : In equation ... (1) if `Delta S to 0`, then
`phi = oint overset(to) (B) . overset(to) (dS) =0`
This equation is also a Gauss.s law.