# Guass Law

## Homework Statement

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.

ehild
Homework Helper
For part 2 I am stuck both b and c.

I got [(KQR^4)/((a^4)(r^2))] which is incorrect.

ehild

r is what I got with determining K. I got $$\frac{1}{4\pi \epsilon_0 r^2},$$ but I replaced the 1/4pi e_0 with K.

vela
Staff Emeritus