# Electric Field of a Spherical Insulator

1. Feb 7, 2013

### Stealth849

1. The problem statement, all variables and given/known data

A spherical insulator of radius R and charge density ρ = ρo/r2 where r is the distance from its centre. Find the electric field at a point inside and outside the insulator.

2. Relevant equations

EA = Qenclo

3. The attempt at a solution

What's throwing me off is the charge density. Setting up a gaussian sphere, I don't know what to do to find Q for the formula.

2. Feb 7, 2013

### ehild

You need to integrate he charge density enclosed in the Gaussian surface.

ehild

3. Feb 7, 2013

### Stealth849

Can you elaborate a little bit?

I'm not too sure what I should be integrating here...

ρ should be in C/m3

To get Q from ρ, I need to cancel the volume... I don't see what to integrate to achieve this though.

Thanks

4. Feb 7, 2013

### ehild

Charge density is the charge of unit volume. If it is constant you get the charge by simply multiplying the volume with the density.
The density varies with the distance from the centre here. But it is constant in a very thin shell.
What is the volume of a shell if its radius is r and thickness Δr?

ehild

5. Feb 7, 2013

### Stealth849

hm,

if i integrate surface area from 0 ro the Radius, that would give me volume..

so if I take the integral of ρ*dA from 0 to R

where dA = 4*pi*r^2*dr ?

6. Feb 7, 2013

### ehild

Yes, that will be the whole charge of the sphere. Calculate the field from it outside the charged sphere.
If the Gaussian surface is inside the charged sphere at distance r' < R from the centre, you need to integrate from 0 to r'.

ehild