Question

A hollow cylinder has a charge q placed at its centre. If $\varphi$ is the electric flux (in $Vm$ ) associated with the curved surface B, the flux linked with the plane surface A is

• A. $\frac{1}{2}\left(\frac{q}{{\epsilon }_0}-\varphi \right)$
• B. $\frac{q}{2{ϵ}_0}$
• C. $\frac{\varphi }{3}$
• D. $\frac{q}{{ϵ}_0}-\varphi$

Answer 1

Answer: (A)

According to Gauss law, ${\varphi }_{total}=\frac{q}{{ϵ}_0}$
Let electric flux linked with surfaces $A,BandC$ are ${\varphi }_A,{\varphi }_B$ and ${\varphi }_C$ respectively. That is
${\varphi }_{total}={\varphi }_A+{\varphi }_B+{\varphi }_C$
Since ${\varphi }_C={\varphi }_A$
$\therefore 2{\varphi }_A+{\varphi }_B={\varphi }_{total}=\frac{q}{{ϵ}_0}$
or ${\varphi }_A=\frac{1}{2}\left(\frac{q}{{\epsilon }_0}-{\varphi }_B\right)$
But ${\varphi }_B=\varphi ($ given $)$
Hence,
${\varphi }_A=\frac{1}{2}\left(\frac{q}{{\epsilon }_0}-\varphi \right)$