A hollow spherical conductor of radius R has a charge Q on it. A small dent on the surface decreases the volume of the spherical conductor by 2%. Assume that the charge density on the surface does not change due to the dent and the electric field in the dent region remains same as other points on the surface.
(a) `Delta E` is the electrostatic energy stored in the electric field in the shallow dent region and E is the total electrostatic energy of the spherical shell. Find the ratio `(Delta E)/(E)`
(b) Using the ratio obtained in part (a) calculate the percentage change in capacitance of the sphere due to the dent.

Answer

(a) `(1)/(150)`
(b) 0.67 %