Question

Define electric flux. Write its S.I. unit.
“Gauss’s law in electrostatics is true for any closed surface, no matter what its shape or size is”. Justify this statement with the help of a suitable example.

Answer 1

Hint :- Electric field, electric field lines and the electric flux are all linked with each other and are defined and used in different forms to understand the concept of electrostatics more deeply and easily. We will see their definitions and units as we proceed further.

Step By Step Answer:
Electric flux - Electric flux is the measure of number of electric field lines passing through any surface .It is a scalar quantity.
It's S.I unit is volt meters.

Gauss Law- It is defined as the total flux linked within a closed surface is equal to the $\dfrac{1}{{{\varepsilon _0}}}$ times the total charge enclosed by that surface.

Mathematically it is defined as
$\phi = \dfrac{q}{{{\varepsilon _0}}}$

Where

$q =$ Charge enclosed in the surface
${\varepsilon _0} =$permittivity of the vacuum.

The Gaussian surface can be of any shape and size because it’s only the amount of flux coming out of the charge distribution on which we have to concentrate and these will be the same if allowed to pass through any shape and size of surface. It's like a cloud coming out from any three dimensional surface.We use this gauss law in order to find the magnitude of the electric field at any point due to charge distribution.

Note- We mostly choose a surface on which the rays of flux remain either parallel or perpendicular and identical at all points that will be easy to carry integration easily and thus we mostly choose cylindrical or spherical surfaces . We are free to choose any type of Gaussian surface but integration of cylindrical and spherical surfaces becomes very easy.