question_answer

Two concentric spherical shells, made of copper, have radii r and\[R(R>r)\]and carry changes q and Q respectively. The potential at the surface of the inner spherical shell will be zero if Q is equal to

A)  \[-\frac{(r+R)}{r}q\]

B)  \[\frac{(r-R)}{r}q\]

C)  \[-\frac{R}{r}q\]

D)  \[\frac{r}{R}q\]

Correct Answer: C

Solution :

 : Potential at surface\[=\frac{q}{r}\] \[\therefore \] \[{{V}_{1}}=q/r\] Potential at an inside point of a conducting sphere is equal to potential at its surface. \[\therefore \]Due to bigger sphere, \[{{V}_{2}}=\frac{Q}{R}\] \[V={{V}_{1}}+{{V}_{2}}\] Or \[0=\frac{q}{r}+\frac{Q}{R}\] Or \[Q=-\frac{qR}{r}=-\frac{R}{r}q\]