Solve Gauss' Law Problem: Electric Field at P on Spherical Shell

[mujadeo]

Homework Statement

An insulator in the shape of a spherical shell is shown in cross-section above. (see attached .gif) The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 mC (1 mC = 10-6 C). (You may assume that the charge is distributed uniformly throughout the volume of the insulator).

What is Ey, the y-component of the electric field at point P which is located at (x,y) = (0, -5 cm) as shown in the diagram?

Homework Equations

I can't do this I am totally stuck.

The Attempt at a Solution

OK so obviously gauss law.
I chose sphere inside the sphere, of radius 4cm for my gauss surface
i need to calc the charge in this enclosed sphere.

So charge in the sphere should be:

Qin = (r^3 / (R^3 - r^3))*Q

= 7.2e-5

this much is wrong but don't know why
please help --thanks

Heres the drawing on flickr:
http://www.flickr.com/photos/15315161@N02/1607125471/

 

[learningphysics]

can't see the attachment... but I assume (0, -5cm) is located at a radius of 5cm from the center? If I'm wrong about this let me know.

So using Gauss' law... what is the volume of the insulator enclosed within a radius of 5cm?