# Electric field between two spheres

1. Mar 17, 2013

### DrummingAtom

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

If the inner sphere of radius a has charge +Q and the outer sphere of radius b has charge -Q/2. What's the electric field between them?

3. The attempt at a solution

If I use Gauss' law then I would have E*4*pi*a^2 = Q/ε then just solve for E. Is that correct? It seems like the outer sphere would affect the E-field on the inner sphere. By the way, they don't say that these are conducting spheres.

Thanks for any help.

2. Mar 17, 2013

### rude man

You have the field at r = a correct, but what about a < r < b? No, the outer sphere does no affect the E field on the inner sphere. Believe in Dr. Gauss! And also no, it doesn't matter if the sphers are conducting or insulators in this case.

3. Mar 17, 2013

### DrummingAtom

Thanks for the reply. Is this the E-field between the two spheres:

E = Q/(ε*4*pi*r^2) for a < r < b ?

I'm still confused how the outer sphere doesn't affect the E-field between them..

4. Mar 18, 2013

### rude man

Right.

For the same reason that, if you go inside the Earth, the only part exerting gravity on you is the part below you.

At a point r in your sphere, some of the charges outside r will set up a + field and others will set up a - field. Some will push a test charge at r one way, others the opposite way. The net result is complete cancellation of each others' fields. It's not an easy task to do that integration, so again - believe Dr. Gauss!

5. Mar 18, 2013

### SammyS

Staff Emeritus
There are several additional pieces of information needed before this problem could possibly be solved.

Questions:
Are the spheres concentric? (Do they have a common center?)

Is the outer sphere actually a spherical shell? -- That's was is implied, seemingly.

Is the charge distributed uniformly? -- or at least in some sort of symmetrical manner

Suppose you have a uniformly charged spherical shell. What is the electric field inside the shell?
This situation is often covered even before introducing Gauss's Law. ​