Question

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

• A. Zero
• B. $\pi R^{2}E$
• C. $2\pi R^{2}E$
• D. $\frac{E}{\pi R^2}$

Answer 1

The correct option is A Zero


As the cylinder is closed so, the total flux ${\varphi }_{\text{total}}$ passing through the flux will be zero.i.e.,
${\varphi }_{\text{total}}=0$

Cylinder have two circular faces $\text{A}$ and $\text{B}$ and a curved surface as shown in figure. So
${\varphi }_{\text{total}}={\varphi }_A+{\varphi }_B+{\varphi }_{\text{curved}}\dots \dots \left(1\right)$



For face $\text{A}:$

Electric flux ${\varphi }_A=-EA[\because \theta ={180}^{\circ }]$

For face $\text{B}:$

Electric flux, ${\varphi }_B=EA[\because \varphi =0^{\circ }]$

So the net electric flux through circular faces,
${\varphi }_{\text{total}}={\varphi }_{\text{curved}}+-EA+EA=0$

Now, from $\left(1\right)$, ${\varphi }_{\text{curved}}=0$

$\text{Alternative Method}:$
Since none of the field lines are actually cutting the curved surface so flux is zero.

Hence, option (a) is correct answer.