Q179 / 200 · WBJEE 2014 · Physics

Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}\left(r_{2}>r_{1}\right)$. If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is

  • A
    $\frac{-r_{2}}{5}, q$
  • B
    zero
  • Correct answer
    C
    $\frac{-r_{1}}{r_{2}} q$
  • D
    $-q$

Solution

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

Hence, the correct answer is option: 'C'.

Relevant Questions