Question

A hollow cylinder has a charge $qC$ within it. If $\varphi$ is the electric flux in units of $Vm$ associated with the curved surface B, the flux linked with the plane surface A in units of $Vm$ will be

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

Answer 1

The correct option is A $\frac{1}{2}(\frac{q}{{ϵ}_0}-\varphi )$

Total flux from all surface of cylinder is ${\varphi }_o=\frac{q}{{ϵ}_o}$

Now,let flux linked with surface A, B and C are ${\varphi }_A,{\varphi }_B$ and ${\varphi }_c$.

Since, A and C are plane faces with same area and are parallel, ${\varphi }_A={\varphi }_B$

And it is given that flux through curved surface which is surface B is ${\varphi }_B=\varphi$

${\varphi }_o={\varphi }_A+{\varphi }_B+{\varphi }_c$

$⟹2{\varphi }_A+\varphi ={\varphi }_o$

$⟹{\varphi }_A=\frac{1}{2}(\frac{q}{{ϵ}_o}-\varphi )$

Answer-(A)