A solid insulating sphere of radius R is charged so that the charge density is proportional to the distance to the center, p(r)=kr, where k is a constant.
Find Q(r), the charge enclosed by a concentric spherical surface of radius r<= R. What is the total charge of the sphere?
The Attempt at a Solution
I thought that Q=[Int from 0 to r] kr dV, and in spherical coordinates for radius, dV = r^2 dr.
So I have Q=[int from 0 to r] kr^3 dr = k [int, 0, r] r^3 dr = kr^4 / 4