Question

Gauss's law is valid for

• A. Only regular closed surface
• B. Open surface only
• C. Closed surface only
• D. Only irregular open surface

Answer 1

The correct option is C

Closed surface only

Explanation of Gauss Law:

1. Gauss showed that an important relationship exists between the total electric flux over a closed surface and the total charge enclosed by the surface.
2. Gauss law states that - “In an arbitrary electrostatic field (in vacuum) the total flux over any closed surface is equal to $\frac{1}{{\epsilon }_0}$ times the total charge enclosed by the surface, where ${\epsilon }_0$ is the permittivity of free space."
3. For a closed surface $S$ enclosing $N$ number of point charges $q_1,q_2,.....,q_N$ the law may be expressed mathematically as

${\oint }_S\overrightarrow{E}.d\overrightarrow{S}=\frac{1}{{\epsilon }_0}\times \sum _{i=1}^N{q}_i$

4. For a continuous distribution of charge within a volume $V$ enclosed $S$ and characterized by a volume charge density $\rho$ the law may be written as

${\oint }_S\overrightarrow{E}.d\overrightarrow{S}=\frac{1}{{\epsilon }_0}{\int }_V\rho dV$

Hence, Gauss Law is valid for closed surfaces only, and therefore option $\left(C\right)$ is the correct answer.