Find out energy stored inside a solid non-conducting sphere of total charge Q and radius R. [Assume charge is uniformly distributed in its volume.]

Explanation

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.
`:. U_("inside")= int_(0)^(R)1/2 epsi_(0) E^(2) dV`
Consider an elementary shell of thickness dx and radius x.
Volume of the shell `=(4pi x^(2) dx)`
`U_("inside")=int_(0)^(R) 1/2 epsi_(0) [(KQx)/R^(3)]^(2). 4 pix^(2)dx=1/2 epsi_(0) (K^(2)Q^(2) 4 pi)/R^(6) int_(0)^(R) x^(4) dx`
`=(4pi epsi_(0))/(2R^(6)) Q^(2)/((4pi epsi_(0))^(2)). R^(5)/5=Q^(2)/(40 pi epsi_(0) R)=(KQ^(2))/(10 R)`.