Question

When a $10\mu$C charge is enclosed by a closed surface, the flux passing through the surface is $\varphi$. Now another $10\mu$C charge is placed inside the closed surface, then the flux passing through the surface is _________.

• A. $4\varphi$
• B. $\varphi$
• C. $2\varphi$
• D. Zero

Answer 1

The correct option is C $2\varphi$

Case 1 :
Total charge enclosed $Q=10\mu C$
Flux through the surface $\varphi =\frac{Q}{{ϵ}_o}=\frac{10\mu C}{{ϵ}_o}$
Case 2 :
Total charge enclosed $Q^{\prime }=10+10=20\mu C$
Flux through the surface ${\varphi }^{\prime }=\frac{Q^{\prime }}{{ϵ}_o}=\frac{20\mu C}{{ϵ}_o}=2\varphi$
Correct answer is option C.