I. A non-conducting sphere of radius a has a spherically symmetric, but non-uniform charge distribution is placed on it, given by the volume density function: p(r) = C·r, where C is a positive constant, and 0 < r < a.
a. Find an algebraic expression for the total charge Q on the sphere, in terms of the parameters C and a.
II. Use Gauss' Law to find an algebraic expression for the magnitude of the electric field at a distance R from the origin, in each of the following regions. Express your answer in terms of the following four parameters: the electrostatic constant k; the radius a of the sphere; the total charge Q on the sphere; and the radial distance R from the origin to the field point.
b. Within the insulating sphere (i.e. for R <a):
c. Outside the sphere (i.e. for R > a):
The Attempt at a Solution
I got Q = Cpi(a^4) for part a which is correct.
For part 2 I am stuck both b and c.
I got [(KQR^4)/((a^4)(r^2))] which is incorrect.