# Electric field inside a parallel plate capacitor

• beardo34
In summary, Gauss' law tells you that the electric field inside a charged spherical shell is zero because there is no charge enclosed inside the shell.
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.

beardo34 said:
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

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.

beardo34 said:
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).

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

## 1. What is an electric field?

The electric field is a physical quantity that describes the force experienced by a charged particle in an electric field. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is the electric field inside a parallel plate capacitor calculated?

The electric field inside a parallel plate capacitor can be calculated using the equation E = V/d, where E is the electric field, V is the potential difference between the plates, and d is the distance between the plates.

## 3. Is the electric field uniform inside a parallel plate capacitor?

Yes, the electric field inside a parallel plate capacitor is uniform, meaning it has the same magnitude and direction at all points between the plates. This is because the plates are parallel and the electric field lines are perpendicular to the plates.

## 4. How does the distance between the plates affect the electric field inside a parallel plate capacitor?

The electric field inside a parallel plate capacitor is inversely proportional to the distance between the plates. This means that as the distance between the plates increases, the electric field decreases, and vice versa.

## 5. Can the electric field inside a parallel plate capacitor be zero?

Yes, the electric field inside a parallel plate capacitor can be zero if the potential difference between the plates is also zero. This can occur if the plates are connected to an external voltage source, such as a battery, with the same potential difference.

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