Question

ratio of electrostatic potential energy of a shell to a non conducting sphere​

Answer 1

We can charge solid sphere to be made of large number of concentric spherical shells. Also electric field intensity at the location of any particular shell is constant.

Uinside = ∫(ul) R (ll) 0 ε0 E^2 dv

Consider an elementary shell of thickness dx and radius x.

Volume of shell = 4πx^2dx

(See the attachment)

Answer 2

Ratio of electrostatic potential energy of shell and non conducting sphere = 2:1

Explanation:

When the thickness of the shell is negligible, the potential energy at the center is kq/R where k is the constant (9 *10^9 N), q is the amount of charge present and R is the radius of the the shell.

In case of a non-conducting sphere, given that the same charge, its distribution is given by kq/2R.

So the ratio of electrostatic potential energy of shell and non-conducting sphere = kq/R  : kq/2R = 2:1.