Find Electric Field Around a Non-Conducting Sphere

[tuggler]

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]

For part 2 I am stuck both b and c.

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

Is this your answer for b) or c)? What is r in your formula?

ehild

 

[tuggler]

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]

What does $r$ represent physically? $R$ is the distance from the center of the sphere; $a$ is the radius of the sphere. What is $r$?

You need to show your work. Just posting an incorrect answer is next to useless for us to see where you're getting stuck.