Use Gauss' Law to find the electric field

[latentcorpse]

Use Gauss' Law to find the electric field, everywhere,of charge of uniform density \rho occupying the region a<r<b, where r is the distance from the origin. Having done this, find the potential.

Ok, so far I said that by Gauss' Law,

\Phi=\oint_S \vec{E} \cdot \vec{dS} = \int_V \nabla \cdot \vec{E} dV = \frac{Q}{\epsilon_0} = \frac{1}{\epsilon_0} \int_V \rho dV

and since V is arbitrary I obtain Poisson's Equation
\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}

I just can't see how to rearrange for E?

Initially I was considering integrating something over a sphere of radius b and then over a sphere of radius a and subtracting them but I don't have any idea what to integrate.

Are either of these ideas useful? If so, what do I do next? If not, can you suggest something?

Cheers

 

[chrisk]

What is a and b? If you are calculating the E field inside the uniformly charged sphere then the charge enclosed by the Gaussian surface is a function of the radius. Outside the sphere it can be treated as a point charge. The potential then can be found between the points a and b.

 

[turin]

Don't ignore the most important point of the problem. There is a symmetry that tells you the direction of E (+ or -) at every point in space, and that the magnitude of E is independent of two certain generalized coordinates.