Question

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

• A. $2\pi R^{2}E$
• B. $\frac{\pi R^2}{E}$
• C. $\pi (R^2-Rl)E$
• D. $0$

Answer 1

The correct option is D $0$

Given , a cylinder of length $l$ and radius $R$ in a uniform electric field parallel to its axis.

Let ${\varphi }_1$ and ${\varphi }_2$ be the flux coming out of a circular cross-sectional surface. ${\varphi }_3$ is flux through the curved surface. Since, normal to curved surface is always at ${90}^{\circ }$ to $\overrightarrow{E}$, so ${\varphi }_3=Ed{S}_3\cos \theta =3d{S}_3\cos {90}^{\circ }=0$

${\varphi }_1$ and ${\varphi }_2$ are equal and opposite so ${\varphi }_1+{\varphi }_2=0$

So, total flux through the surface of cylinder is zero.