# Electrostatics conductor problem

1. Feb 10, 2008

### ehrenfest

[SOLVED] electrostatics problem

1. The problem statement, all variables and given/known data
Two spherical cavities, of radii a and b, are hollowed out from the interior of a (neutral) conducting sphere of radius R. At the center of each cavity a point charge is placed--call these charges q_a and q_b.
Why is it necessarily true that the force on q_a and q_b is 0? Why is it true that the force is still zero no matter what kind of charge distribution you have outside the conductor.

2. Relevant equations

3. The attempt at a solution
You can use Gauss's Law to find the electric field in each cavity. And you find that it is as the charge were isolated in space. But that doesn't tell you the electric field at the charge...only around it, right?

2. Feb 10, 2008

### jacobrhcp

*is a little rusty on the subject*

conducting sphere means that, if there is an electric field in the conducting sphere, then the electrons in the conducting sphere will move as to create an electric field to cancel the electric field in place, right?

That would answer you question, because E=0 => F=0

3. Feb 10, 2008

### ehrenfest

But q_a and q_b are in cavities, not in the meat of the conductor.

4. Feb 10, 2008

### pam

Draw a Gaussian sphere in the conductor, just outside one cavity. The E field is zero everywhere on the sphere. This can only happen if the surface charge on the inside of the cavity is spherically symmetric, i.e. constant. Then the field at the center of the spherical cavity will be zero, giving zero force on the point charge. This only happens at the center of the cavity. There would be a force on a charge at other points in the cavity.

5. Feb 10, 2008

### kdv

I was going to say exactly the same thing.