A uniformly charged solid non-conducting sphere of radius R has an electrostatic potential V₀ at its surface. The distance from the centre of the sphere where the electrostatic potential is 5 4 V₀ will be:

Step-by-step solution

The electrostatic potential at the surface of a uniformly charged solid sphere of radius R is given by: V₀ = kQ R The potential at a distance r ( r R ) from the centre is given by: V(r) = kQ 2R^3 (3R^2 - r^2) Substituting kQ = V₀ R , we get: V(r) = V₀ 2R^2 (3R^2 - r^2) We are given that V(r) = 5 4 V₀ . Equating the two expressions: V₀ 2R^2 (3R^2 - r^2) = 5 4 V₀ 3R^2 - r^2 2R^2 = 5 4 3R^2 - r^2 = 5 2 R^2 r^2 = 3R^2 - 2.5R^2 = 0.5R^2 = R^2 2 r = R 2 Answer: R 2