# Field between 2 conducting spheres in electric field

1. Nov 8, 2011

### oliverroth

Hi,
I tried to make some simulations of two conducting spheres in a constant electric field. The simulations seem to indicate that the electric field in the gap increases with increasing diameter of the spheres at a constant gap distance. Does this make sense? I expected just the reverse. What is wrong? Does an analytical solution for this problem exist?
I really appreciate any help.

2. Nov 8, 2011

### clem

If I approximate the added field at the center of the gap as due to two induced dipoles,
I get $$E=\frac{4E_0}{(1+d/2R)^3}$$. This agrees with what you found.

3. Nov 8, 2011

### oliverroth

Thanx a lot. This matches qualitatively (although it still sounds odd to me). Can you tell me how you have derived this result?

4. Nov 8, 2011

### clem

A conducting sphere in constant electric field E_0 gets an induced dipole moment
$$p=E_0 R^3.$$. The electric field a distance R+d/2 from a dipole is
$$E=2p/(R+d/2)^3.$$ Put these together to get the answer.

5. Nov 9, 2011

### oliverroth

Ok. Thank you.