Superposition of Spherical Charge Distributions

[physicsphan89]

Homework Statement

http://photos-e.ak.fbcdn.net/hphotos-ak-snc1/hs031.snc1/2658_1060058793594_1589658877_146788_3259033_n.jpg

Homework Equations

The Attempt at a Solution

So I know that I should use the superposition principle, and treat it as 2 superimposed spheres of opposite charge densities. I can use Gauss's law to find the electric field of each. However I am having a little trouble figuring out how to take into account the fact that the spheres are not concentric. I also don't know whether to use the electric field inside or outside the spheres.

 

[gabbagabbahey]

Homework Statement

http://photos-e.ak.fbcdn.net/hphotos-ak-snc1/hs031.snc1/2658_1060058793594_1589658877_146788_3259033_n.jpg

Homework Equations

The Attempt at a Solution

So I know that I should use the superposition principle, and treat it as 2 superimposed spheres of opposite charge densities. I can use Gauss's law to find the electric field of each. However I am having a little trouble figuring out how to take into account the fact that the spheres are not concentric. I also don't know whether to use the electric field inside or outside the spheres.

Well, you are interested in finding the electric field inside the cavity, that region lies within both the large sphere and the small sphere, so you want to use the fields inside each sphere.

What do you get for the individual fields fields, in vector form, inside the spheres?