A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

• A

  $2 \pi R^2 E$
• B

  $\frac{\pi R^2}{E}$
• C

  $\frac{R}{E}$
• Correct answer
  D

  zero

Solution

Flux through surface $A$, $\begin{aligned} & \phi_A=E \times \pi R^2 \\ & \phi_B=-E \times \pi R^2\end{aligned}$ Flux through curved surface, $C=\int E \cdot d S$ $=\int E d S \cos 90^{\circ}=0$ $\therefore$ Total flux through cylinder $=\phi_A+\phi_B+\phi_C=0$

Hence, the correct answer is option: 'D'.