Question

Consider two concentric spherical metal shells of radii $r_1$ and $r_2$ $(r_2 > r_1)$. If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is

• A. $-\frac{r_{2}}{r_{1}}q$
• B. zero
• C. $-\frac{r_{1}}{r_{2}}q$
• D. $-q$

Answer 1

Answer: (C)

Since the inner shell is grounded, therefore, its potential is zero. Let $q$' be charge on the inner shell. Then
$V_{inner}=\frac{1}{4\pi\varepsilon_{0}} \left(\frac{q'}{r_{1}}+\frac{q}{r_{2}}\right)=0$
or $ \frac{q'}{r_{1}}+\frac{q}{r_{2}}=0$
or $q' =-\frac{r_{1}}{r_{2}}q$