Is the Electric Field Zero Inside Any Shape of an Empty Cavity in a Conductor?

[hisashiburi]

Homework Statement

The electric field inside an empty cavity in a conductor is zero. Is this statement true no matter what the shape of the cavity? Why or why not?

Homework Equations

Electric field equation. E = kQ / R^2

The Attempt at a Solution

I can't seem to figure out if this is true no matter what the shape.

 

[jacobrhcp]

no, consider a charge in a cavity in a conductor.

it's only in the meat of the conductor, because when you would put a conductor in a field, the electrons would move and create a field with the protons on their own. The two fields tend to cancel. But in a hole, you don't have this problem. (The edges of the conductor will be charged however, in that case.)

 

[Dick]

no, consider a charge in a cavity in a conductor.

it's only in the meat of the conductor, because when you would put a conductor in a field, the electrons would move and create a field with the protons on their own. The two fields tend to cancel. But in a hole, you don't have this problem. (The edges of the conductor will be charged however, in that case.)

That's correct, but it's stated that the cavity is empty, so it doesn't contain a charge. There's no net charge density in the conductor and the cavity is empty, so the only place a charge could be is on the surface of the cavity. Now consider a gaussian surface around the cavity but inside the conductor.

 

[jacobrhcp]

oh I'm sorry, ah well... I guess Dick gave you quite a hint there.