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## Homework Statement

A one-sided conductor plate with negligible thickness and infinite dimension is charged to a voltage of V via electrostatic induction.

Assuming charge is distributed evenly on the surface of the conductor, describe if and how the voltage relates to charge distribution.

## Homework Equations

## The Attempt at a Solution

I have no clear route to the answer. What i do know is that first of all the electric field directly at the surface in a statically charged object is perpendicular and equal everywhere and can be determined to be, using Gauss' law,

E = 2*pi*k*a, where k = 9*10^9 and a = surface charge density

Then, I need to somehow relate voltage to an electric field.

So I think of the formula -V = integral of E

**in terms of x. But of course i don't have a function of E in terms of x.**

*function*Trying to find one, I use the electric field a distance

**Z**from a charged disk with radius

**R**(I got it from the website

lightandmatter.com/html_books/0sn/ch10/ch10.html#Section10.2

, SECTION 10.2 example 12)

E(z component) = 2*pi*k*a*(1-Z/sqrt(R^2+Z^2)). OK, but when I integrate and include the constant of integration, the constant turns out to be the initial voltage on the plate. As Z (distance from disk) approaches 0, the integral I found approaches the constant of integration. So basically, it's telling me voltage on plate = voltage on plate! But I want voltage in terms of charge density!

It goes round and round... How do you relate charge surface density and voltage (or electric field and voltage) on an infinite plate? Something obvious?

Thxs!