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

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

Answer 1

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

R.E.F image

Given ${\varphi }_B=\varphi$

Total Flux $=\frac{1}{{ϵ}_0}$ (change enclosed)

${\varphi }_A+{\varphi }_B+{\varphi }_C=\frac{1}{{ϵ}_0}\times q$

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

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