Q103 / 150 · MHT CET 2021 (20 Sep Shift 2) · Physics

A spherical conducting shell of inner radius ' $r_1$ ' and outer radius ' $r_2$ ' has a charge ' $Q$ '. A charge $-q$ is placed at the center of the shell. The surface charge density on the inner and outer surface of the shell will be Figure

  • Correct answer
    A
    $\frac{\mathrm{q}}{4 \pi \mathrm{r}_1^2}$ and $\frac{\mathrm{Q}-\mathrm{q}}{4 \pi \mathrm{r}_2^2}$
  • B
    $\frac{\mathrm{q}}{4 \pi \mathrm{r}_1^2}$ and $\frac{\mathrm{Q}}{4 \pi \mathrm{r}_2^2}$
  • C
    $\frac{-\mathrm{q}}{4 \pi \mathrm{r}_1^2}$ and $\frac{\mathrm{Q}+\mathrm{q}}{4 \pi \mathrm{r}_2^2}$
  • D
    zero and $\frac{\mathrm{Q}-\mathrm{q}}{4 \pi \mathrm{r}_2^2}$

Solution

Due to charge $-q$ at the center of the shell, a charge $q$ will be induced on the inner surface and $-q$ on the outer surface. The charge on outer surface will become $Q-q$. Hence surface charge densities will be $\frac{\mathrm{q}}{4 \pi \mathrm{r}_1^2}$ and $\frac{\mathrm{Q}-\mathrm{q}}{4 \pi \mathrm{r}_2^2}$

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

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