Electric Field of a Spherical Insulator

[Stealth849]

Homework Statement

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

Homework Equations

EA = Q_encl/ε_o

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.

 

[ehild]

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

ehild

 

[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

 

[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

 

[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 ?

 

[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