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)

Let, the charge on the inner shell be $q^{'}$
The total charge will be zero
So, $ \frac{k q^{'}}{r_{1}}+\frac{k q}{r_{2}}=0 \left(\because r_{2} > r_{1}\right) $
$\Rightarrow q^{'}=-\frac{K q / r_{2}}{K / r_{1}} $
$ q^{'}=-\left(\frac{r_{1}}{r_{2}}\right) q$