The electric field inside a hole inside a conductor is still 0?

[Eitan Levy]

Homework Statement

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Relevant Equations

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This is not a homework question but something that bugs me a bit.

My professor has stated that the electric field inside a conductor is 0. This I understand.

However, he has also said that even if the conductor has some hole in it, the electric field inside this hole is also 0

Now, two examples which confuse me:

Consider a thick spherical shell with radiuses a,b. Now, let there be a point charge q outside the shell. It is said the the electric field inside the shell is 0 due to the reason above.

However, if we move the charge to the center of the shell, it is said that the electric field inside the shell is kq/r^2, which is different than 0.

I am quite confused. Is the statement only correct when there are no charges inside the hole?

Another quick question: If the shell isn't thick, is the electric field inside still 0 for the first example? I believe it is but am not sure.

 

[etotheipi]

I rephrase. Two theorems:

1. The electric field inside a uniformly charged shell, due to that uniformly charged shell, is zero.
2. The electric field from multiple sources is the sum of the electric fields from those sources individually (principle of superposition).

Conducting shells are tricky, since charges redistribute within them in response to applied fields. The conducting shell will likely not be uniformly charged anymore if you introduce a charge to the configuration space, so the electric field inside the shell due to the shell is no longer constrained to be zero by the shell theorem!

However if the additional charge is outside the shell, then the shell acts as a Faraday cage, and the electric field inside the shell will still be zero.

If you introduce an additional charge inside the conducting shell, then the electric field inside the shell will be non-zero.

 

[TSny]

My professor has stated that the electric field inside a conductor is 0. This I understand.

However, he has also said that even if the conductor has some hole in it, the electric field inside this hole is also 0

Is the statement only correct when there are no charges inside the hole?

Yes, it is only true if there are no charges inside the cavity.

Another quick question: If the shell isn't thick, is the electric field inside still 0 for the first example? I believe it is but am not sure.

E will be 0 no matter the thickness of the shell.

One way to argue that E must be zero at each point of an empty cavity of a conductor in electrostatic equilibrium is as follows. If there is an electric field line inside the cavity, then the line must begin at some point, $a$, on the wall of the cavity, and end at some other point, $b$, of the cavity. Recall that if you move along an electric field line in the direction of the field, the electric potential $V$ must decrease. Thus, this would imply that point $b$ is at a lower potential than point $a$. But this would violate the condition that all points of a conductor in electrostatic equilibrium must be at the same potential.