Question

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

• A. $\frac{ q }{2 \epsilon_{0}}$
• B. $\frac{\phi}{3}$
• C. $\frac{ q }{\epsilon_{0}}-\phi$
• D. $\frac{1}{2}\left(\frac{ q }{\epsilon_{0}}-\phi\right)$

Answer 1

Answer: (D)

$\frac{1}{2}\left(\frac{ q }{\epsilon_{0}}-\phi\right)$

Answer 2

$\phi_{\text {total }}=\phi_{\text {curved }}+\phi_{\text {plane surfaces }}=\frac{ q }{\epsilon_{0}}$
$\phi+2 \phi_{ A }-\frac{ q }{\epsilon_{0}}$
$\Rightarrow \phi_{ A }-\frac{1}{2}\left(\frac{ q }{\epsilon_{0}}-\phi\right)$