Question

A hollow cylinder has a charge q coulomb within it. If $\varphi$ is the electric flux in units of volt-meter associated with the curved surface B, the flux linked with the plane surface A in units of volt-meter will be?

Answer 1

Here, let the flux on A, B, C surfaces be ${\varphi }_A$, ${\varphi }_B$ and ${\varphi }_C$

Then, ${\varphi }_n$${}_e$${}_t$= ${\varphi }_A$ + ${\varphi }_B$ + ${\varphi }_C$ = $\frac{q}{{ϵ}_0}$

So, 2${\varphi }_A$ + $\varphi$ = $\frac{q}{{ϵ}_0}$

${\varphi }_A$ = $\frac{1}{2}$ ($\frac{q}{{ϵ}_0}$ - $\varphi$)

Hence the electric flux through the plane surface is $\frac{1}{2}$ ($\frac{q}{{ϵ}_0}$ - $\varphi$)