# Electric field of a positive plate

1. Homework Statement
There is a large positively charged plate whose charge density is $\sigma = 2.0 × 10^{-5}\frac{C}{m^2}$. What is the electric field at a point P, that is not enclosed between the plates.

2. Homework Equations
For an infinite sheet:
$$\vec E = \frac{\sigma}{2\varepsilon_0}\hat r$$

3. The Attempt at a Solution
I thought to find the field of the plate by adding, but that would be the field between two infinite planes, one with negative charge and one with a positive charge. Would that still form the electric field of a positively charged plate? So,
$$\vec E = \frac{\sigma}{\varepsilon_0}\hat r$$

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TSny
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Hello. Can you clarify the problem statement? The first sentence seems to imply that there is only one plate. The second sentence implies more than one plate.

There is one plate. The plate has three dimensions, while the sheet only has two. So there is a thickness to the plate that the sheet does not have.

Hello. Can you clarify the problem statement? The first sentence seems to imply that there is only one plate. The second sentence implies more than one plate.
The plate has a thickness, so it is in three dimensions. The sheet is only two dimensional, so it would be a plane in a 3D space.

TSny
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There is one plate. The plate has three dimensions, while the sheet only has two. So there is a thickness to the plate that the sheet does not have.
So you have a single plate that has some thickness to it? What does it mean when the problem statement says that point P is not between the plates?

Last edited:
Well I did not state the full problem, but if it helps here's an image. Part of the problem was finding the electric field to find the force, and once I find that I know how to continue. So the proton is not between the two sheets which form the plates.

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TSny
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OK, that helps. Point P is not between the faces of the plate. In the problem statement, you say that $\sigma$ is the charge density of the plate. Does that mean that each face of the plate has the surface charge $\sigma$?

I think it would be helpful to state the relevant part of the problem word for word.
See the paragraph for item 3 here: https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/

The whole problem is:
From a distance of 10 cm, a proton is projected with a speed of v = 4.0 × 106 m/s directly at a large, positively charged plate whose charge density is $\sigma = 2.0 × 10^{−5}C/m^22$. (See below.) (a) Does the proton reach the plate? (b) If not, how far from the plate does it turn around?

So from my understanding, $\sigma$ would be the surface charge of each plate.

TSny
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Thank you. You have the right idea that you sum the contributions from each surface (sheet of charge). Your expression for E in the "attempt at a solution" is correct, although I'm not sure what the unit vector $\hat r$ denotes?

$\hat r$ would be the direction of the field.

Thank you.

TSny
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$\hat r$ would be the direction of the field.
And what direction would that be?

In this case it would be in the $-\hat i$ direction acting on the proton.

TSny
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In this case it would be in the $-\hat i$ direction acting on the proton.
OK. Good. I think you have it.