A hollow metal sphere of radius 10 cm is uniformly charged such that the electric potential at a distance of 20 cm from the center is 10 V. The electric potential at a distance of 5 cm from the center of the sphere will be

20 V

The correct answer is Option (2) → 20 V

$\text{Given: Radius of sphere } R = 10~\text{cm} = 0.1~\text{m}$

$\text{Potential at } r = 20~\text{cm} = 0.2~\text{m is } V = 10~\text{V}$

$\text{Potential outside a charged sphere: } V = \frac{k Q}{r}$

$10 = \frac{(9 \times 10^9) Q}{0.2}$

$Q = \frac{10 \cdot 0.2}{9 \times 10^9}$

$Q = \frac{2}{9 \times 10^9} \approx 2.22 \times 10^{-10}~\text{C}$

$\text{Potential at a point inside the hollow sphere (r < R) is same as on the surface: } V = \frac{k Q}{R}$

$V = \frac{9 \times 10^9 \cdot 2.22 \times 10^{-10}}{0.1}$

$V \approx 20~\text{V}$

$\text{Answer: } V = 20~\text{V}$