Consider three concentric metallic spheres A, B and C of radii a, b, c respectively where a $ < \mathrm{b} < \mathrm{c}, \mathrm{A}$ and $\mathrm{B}$ are connected whereas $\mathrm{C}$ is grounded. The potential of the middle sphere $\mathrm{B}$ is raised to $\mathrm{V}$ then the charge on the sphere C is-

• Correct answer
  A

  $-4 \pi \varepsilon_{0} \mathrm{~V} \frac{\mathrm{bc}}{\mathrm{c}-\mathrm{h}}$
• B

  $-4 \pi \varepsilon_{0} \mathrm{~V} \frac{\mathrm{ac}}{\mathrm{c}-\mathrm{a}}$
• C

  $+4 \pi \varepsilon_{0} \mathrm{~V} \frac{\mathrm{bc}}{\mathrm{c}-\mathrm{b}}$
• D

  zero

Solution

$\mathrm{V}_{\mathrm{B}}=\frac{\mathrm{kq}}{\mathrm{b}}+\frac{\mathrm{k}(-\mathrm{q})}{\mathrm{c}}=\mathrm{V} \text { (Given) }$ $\mathrm{q}=\frac{4 \pi \varepsilon_{0} \cdot \mathrm{bc}}{\mathrm{c}-\mathrm{b}} \cdot \mathrm{V}$ Charge on $\mathrm{C}=-\mathrm{q}$

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