Question

Electric filed at point $P$ is given by $\vec{ E }= r \vec{ E }_{0} .$ The total flux through the given cylinder of radius $R$ and height h is:

• A. $E _{0} \pi R ^{2} h$
• B. $2 E _{0} \pi R ^{2} h$
• C. $3 E _{0} \pi R ^{2} h$
• D. $4 E_0 \pi R ^{2} h$

Answer 1

Answer: (C)

As $r=\sqrt{R^{2}+h^{2}}$
$d \phi= E \cdot 2 \pi Rdh \cos \theta$
$\Rightarrow d \phi=2 \pi E _{0} R ^{2} h$
$\Rightarrow \phi=2 \pi E _{0} R ^{2} h$
For upperface $rE _{0} \cdot 2 \pi rdr \cos \theta$
$\Rightarrow \phi_{2}=\pi E _{0} R ^{2} h$
$\Rightarrow \phi_{\text {total }}=3 E _{0} \pi R ^{2} h$