# Determining the electric potential at a distance

1. Homework Statement

The electric potential of a very large isolated flat metal plate is 2000 V. The plate carries a uniform distribution of charge with surface density σ=1 μC/m2. Determine potential V at a distance x=1 cm from the plate. Assume that point x is far from the edges and that x is much smaller than the size of the plate.

2. Homework Equations

To find the magnitude of the electric field I know I have to use: |E|=σ/2ϵ0

3. The Attempt at a Solution

I'll be honest I have no clue how to solve this problem, any pointers in the right direction would greatly help!

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#### BruceW

Homework Helper
Well, you've got E, and they are asking for potential, so what equation do you know which connects E and V ?

Would I be wrong in stating that since it's a very large plate with uniform charge density, it isn't a point charge. The formula that I have that links those two informations are:

ΔV = -∫Eds, and since the electric field is constant,

ΔV = -Es

ΔV = -σ/2ϵ0 times s

ΔV = -((1 μC/m2)/(2ε0)) times 0.01m

It seems like it's too simple solving like that, I feel like I'm missing something

Last edited:

#### BruceW

Homework Helper
That is the right answer. The question was more simple than you thought. The final step is to use the initial V and change in V to get the V 1cm away.

I'm not sure I understand what you mean by that last reply

If I read it right: The answer gives me ΔV, and I have VA, I want VB, right?

So I should do: ΔV = VB - VA ==> ΔV (That I found) = VB - 2000V

So ΔV + 2000V = VB (the volt at 1cm away)?

#### BruceW

Homework Helper
yes, that's right.

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