# Electric field inside a parallel plate capacitor

beardo34
Ok I took E&M about 3 years ago and decided I needed to review it. I'm up to gauss' law and am getting confused about one thing. If you have two infinitely long oppositely charged plates, solving for the total e field inside is done by making two gaussian surfaces that enclose each plate. Doing this gives the e field to be a constant between the plates.

My question is, why can't I make a gaussian "pillbox" inside the plates and enclosing zero charge and conclude that the flux through that surface is zero since the field goes in one side and leaves through the other? Obviously I'm making a mistake here somewhere because the field in between the plates is NOT zero but I can't figure out what the mistake is.

Mentor
Ok I took E&M about 3 years ago and decided I needed to review it. I'm up to gauss' law and am getting confused about one thing. If you have two infinitely long oppositely charged plates, solving for the total e field inside is done by making two gaussian surfaces that enclose each plate. Doing this gives the e field to be a constant between the plates.

My question is, why can't I make a gaussian "pillbox" inside the plates and enclosing zero charge and conclude that the flux through that surface is zero since the field goes in one side and leaves through the other? Obviously I'm making a mistake here somewhere because the field in between the plates is NOT zero but I can't figure out what the mistake is.

Sure you can do that. The conclusion from Gauss' law is that the pillbox encloses no charge. This is not an unexpected result

beardo34
Okay but doesn't that mean the electric field inside that pillbox is zero? I am just getting confused because when you have a charged spherical shell, the field inside is zero because there is no charge.

Mentor
Okay but doesn't that mean the electric field inside that pillbox is zero? I am just getting confused because when you have a charged spherical shell, the field inside is zero because there is no charge.

No, you can place such a pillbox anywhere in a given electric field where the enclosed charge is zero, yet there is still a field. This tells you that there is no contribution to the field from inside the pillbox.

The Gaussian surface inside a charged spherical shell tells you the same thing -- no enclosed charge and no contribution from inside the pillbox. The field inside the shell is zero for other reasons (see: Newton's Shell Theorem).

beardo34
Ohh okay, that's what I was missing. Thanks a lot!