Find the charge density inside a solid insulating sphere?

[hockey]

Homework Statement

The electric field at a distance of 0.143m from the surface of a solid insulating sphere with radius 0.381m is 1630N/C .

a) Assuming the sphere's charge is uniformly distributed, what is the charge density inside it?

b) Calculate the electric field inside the sphere at a distance of 0.237m from the center.

Homework Equations

E1/E2 = r1/r2
E = Cr

The Attempt at a Solution

a) I know that the electric field for part a can be found by using the formula E=Cr, so I can get C = 4278.22 N/(C*m). I know that the charge density is a factor of C, but I do not know the actual formula for it.

b) This should be able to be solved with the ratio E1/E2 = r1/r2, and when I solve for E2 I get a result of 737.2 N/C. This result is not correct, but I am not sure if the problem is in my ratio.

 

[Simon Bridge]

a) I know that the electric field for part a can be found by using the formula E=Cr, so I can get C = 4278.22 N/(C*m). I know that the charge density is a factor of C, but I do not know the actual formula for it.

You can figure it out though. Hint: what are the units of charge density?

b) This should be able to be solved with the ratio E1/E2 = r1/r2, and when I solve for E2 I get a result of 737.2 N/C. This result is not correct, but I am not sure if the problem is in my ratio.

Write out the equation for E1 and E2 separately, then find E1/E2.

 

[rude man]

a) 1. figure out what total charge Q is for an E field at the specified location.
2. Q = volumetric charge density x volume gives you charge density.

b) 1. Use Gaussian surface.