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
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 20\,\mathrm{V} \)
Outside a charged sphere the potential is that of a point charge at its centre, \( V = kQ/r \). Inside a hollow conducting sphere the field is zero, so the potential is constant and equal to the value on the surface.
\( \displaystyle \frac{kQ}{0.20\,\mathrm{m}} = 10\,\mathrm{V} \Rightarrow kQ = 2\,\mathrm{V\,m} \)
Potential on the surface (\( r = 10\,\mathrm{cm} = 0.10\,\mathrm{m} \)):
\( \displaystyle V_{\mathrm{surface}} = \frac{kQ}{0.10} = \frac{2}{0.10} = 20\,\mathrm{V} \)
The point at 5 cm lies inside the sphere, so its potential is also \( 20\,\mathrm{V} \).