Question

Gauss's law can help in the easy calculation of electric field due to:

• A. moving charge only.
• B. any charge configuration.
• C. any symmetrical charge configuration.
• D. some special symmetric charge configurations.

Answer 1

The correct option is D some special symmetric charge configurations.

Gauss' law becomes highly useful in the easy calculation of electric field due to a charge configuration, when the distribution is symmetrical and $\overrightarrow{E}$ is normal to the chosen surface such that,
$\oint \overrightarrow{E}\cdot d\overrightarrow{S}=\oint EdS\cos 0^{\circ }$

$\Rightarrow \oint \overrightarrow{E}\cdot d\overrightarrow{S}=E\oint dS=ES$

(since $\overrightarrow{E}$ is radially outwards and parallel to the area vector)

$\therefore$ Symmetric charge distributions where electric field is parallel to the area vector are preferred for applying Gauss' law i.e. sphere, cube, cylinder, etc.