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. $2E_0\pi R^{2}h$
• C. $3E_0\pi R^{2}h$
• D. $4E_0\pi R^{2}h$

Answer 1

Answer: (C)

As $r=\sqrt{R^2+h^2}$
$d\varphi =E\cdot 2\pi Rdh\cos \theta$
$\Rightarrow d\varphi =2\pi E_0{R}^{2}h$
$\Rightarrow \varphi =2\pi E_0{R}^{2}h$
For upperface $r{E}_0\cdot 2\pi rdr\cos \theta$
$\Rightarrow {\varphi }_2=\pi E_0{R}^{2}h$
$\Rightarrow {\varphi }_{\text{total }}=3E_0\pi R^{2}h$