An insulating solid sphere of radius R has a uniformly positive charge density `rho`. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.
Statement-1: When a charge 'q' is taken from the centre to the surface of the sphere, its potential energy changes by `(qrho)/(3 in_(0))`
Statement-2 : The electric field at a distance `r (r lt R)` from the centre of the the sphere is `(rho r)/(3in_(0))`

Options

A. Both Statement-1 & Statement-2 are correct & Statement-2 is the correct explanation of Statement-1
B. Both Statement-1 & Statement-2 are correct & Statement-2 is not the correct explanation of Statement-1
C. Statement - 1 is correct but Statement -2 is incorrect
D. Statement-2 is correct but Statement-1 is incorrect

Answer

D

Explanation

For a solid insulating sphere, potential at centre is `V_(centre) =3/2 (kq)/R` and potential at surface at `V_(surface) =(kq)/R`.
So, change in potential energy when charge q is taken from centre to surface is
`Delta V= U_f-U_i =q (V_f-V_i) =q ((kq)/R-3/2 (kq)/R) =(-q)/2 . 1/(4 pi e_0) (4/3 pi R^3 p)/R= (-q R^2 p)/(6 e_0)`
So, statement 1 is incorrect, while Statement 2 is correct `therefore E(n)=pr//3e_0`