Consider a Gaussian surface of radiussuch thatinside the sphere as shown below:

It is known that the spherical consist the charge density which varies as.So, the charge enclosed by the Gaussian sphere of radius is obtained by integrating the charge density from 0 to, as
Substitute krfor p, for in the equation
localid="1654599163389"
Apply Gauss law on the Gaussian surface, by substituting for , and for dainto
localid="1654343673710"
Thus, the electric field inside the non-uniformly charged solid sphere is
.