In finding the electric field using Gauss's law, the formula $|\vec E| = \dfrac{q_{\text{enc}}}{\varepsilon_0|A|}$ is applicable. In the formula $\varepsilon_0$ is the permittivity of free space, $A$ is the area of the Gaussian surface and $q_{\text{enc}}$ is the charge enclosed by the Gaussian surface. This equation can be used in which of the following situations?
Answer: (B) Only when the Gaussian surface is an equipotential surface and $|\vec E|$ is constant on the surface
Gauss's law says $\oint\vec E\cdot d\vec A = \dfrac{q_{\text{enc}}}{\varepsilon_0}$. It reduces to $|\vec E||A| = \dfrac{q_{\text{enc}}}{\varepsilon_0}$ only if
(i) $\vec E$ is everywhere normal to the surface, which is true when the surface is an equipotential, and
(ii) $|\vec E|$ has the same value everywhere on the surface.
Both conditions are needed.
Solution by Sreeraj P, M.Sc Physics