Question

An electric field is uniform, and in the positive $x$ direction for positive $x$, and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E=200\hat{i}N/C$ for $x>0$ and $E=-200\hat{i}N/C$ for $x<0$. A right circular cylinder of length $20cm$ and radius $5cm$ has its centre at the origin and its axis along the x-xis so that one face is at $x=+10cm$ and the other is at $x=-10cm$.
(a) What is the net outward flux through each flat face?
(b) What is the flux through the side of the cylinder?
(c) What is the net outward flux through the side of the cylinder?

Answer 1

(a) Net $\varphi$ through flat
surface $=\overrightarrow{E}\cdot \overrightarrow{A}[\theta =0^o]$
$=EA\cos \theta$
$=\left(200\right)\left(\pi {0.05}^2\right)$
$=\frac{\pi }{2}\frac{N{m}^2}{C^2}$
$=1.5707\frac{N{m}^2}{C^2}$
(b) Net $\varphi$ through curved
surface $\overrightarrow{E}\cdot \overrightarrow{A}$
$=0[\because \overrightarrow{E}\perp \overrightarrow{A}]$
(c) Net outward flux $=2\times \varphi$ flat surface
$=\pi \frac{N{m}^2}{C^2}$
$=3.14\frac{N{m}^2}{C^2}$