Question

A Gaussian surface in the cylinder of cross section $\pi a^2$ and length $L$ is immersed in a uniform electric field $\overline{E}$ with the cylinder axis parallel to the field. The flux ${}^{\prime }{\varphi }^{\prime }$ of the electric field through the closed surface is:

• A. $2\pi a^2\overline{E}$
• B. $\pi a^2\overline{E}L$
• C. $\pi a^2(2+L)\overline{E}$
• D. Zero

Answer 1

The correct option is D Zero

The electric lines of force would enter from one surface of the cylinder and leave out from the other.

Thus the net flux through the cylinder would be :

$\overrightarrow{B}.\overrightarrow{A_1}+\overrightarrow{B}.\overrightarrow{A_2}$

$B\left(\pi a^2\right)+B(-\pi a^2)=0$