A point charge `q = 3.0 m,uC` is located at the centre of a spherical layer of uniform isotropic dielectric with permittivity `epsilon = 3.0`. The inside radius of the layer is equal to `a = 250 mm`, the outside radius is `b = 500 mm`. Find the electrostatic energy inside the dielectric layer.

Explanation

Consider a small elemental shell of thickness dx.
Volume `=dV=4pix^(2)dx`
Electric field at x `=(Kq)/(x^(2)x)`
electric energy density `=(1)/(2)in_(0)E^(2)=(1)/(2)in_(0)(K^(2)q^(2))/(x^(4)k^(2))`

Thus energy content in the element shell is
`=dE=(1)/(2)in_(0)(K^(2)q^(2))/(x^(4)k^(2))4pix^(2)dx`
`E=underset(a)overset(b)int(4)/(2)in_(0)(K^(2)piq^(2))/(k^(2)x^(4))x^(2)dx`