Question

A large hollow metal sphere of radius R has a small opening at the top. Small drops of mercury, each of radius r and charged to a potential V, fall into sphere. The potential of the sphere become V' after N drops fall into it. Then-

• A. V' = V for any value of N
• B. V' = V for N = $\left( \frac{R}{r} \right)^{2/3}$
• C. V' = V for N = $\left( \frac{R}{r} \right)^{1/3}$
• D. V' = V for N = $\frac{R}{r}$

Answer 1

Answer: (C)

V' = V for N = $\left( \frac{R}{r} \right)^{1/3}$

Answer 2

V = $\frac { \mathrm { kq } } { \mathrm { r } }$

After N drop

potential of hollow sphere = V'

V' = $\frac { \mathrm { kNq } } { \mathrm { R } }$

V' = V ̃ $\frac { \mathrm { kq } } { \mathrm { r } }$ = $\frac { \mathrm { kNq } } { \mathrm { R } }$ ̃ N = $\frac { \mathrm { R } } { \mathrm { r } }$