# Finding the surface charge density

## Homework Statement

A 1.0-mm-diameter wire has 1000 excess electrons per centimeter of length. What is the surface charge density?

## Homework Equations

$$\eta$$ = Q/A

## The Attempt at a Solution

$$\eta$$ = (100000 * 1.6*10^-19)/($$\pi$$ * (5*10^-4)2)
But that gets me 2.037 * 10^-8 C/m^2

The answer is 5.1 * 10^-12 C/m^2

Any ideas?

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Doc Al
Mentor
What's the surface area (not the cross-sectional area) of that section of wire?

Okay, well I'm guessing that this wire is of cylindrical form...
SA = 2pir^2 + 2pirh

the problem is with the height. you might suppose part of that is the diameter...but it's really not. so, i'm still unsure.

Doc Al
Mentor
Okay, well I'm guessing that this wire is of cylindrical form...
SA = 2pir^2 + 2pirh
Don't include the circular end pieces, just the outer surface.

the problem is with the height. you might suppose part of that is the diameter...but it's really not. so, i'm still unsure.
The height corresponds to the length.

Okay.
eta = 10 * 1.6*10^-19 C/(2pi * (5 * 10^-4 m) * (10^-3 m)) = 5.1 * 10^-12 C/m^2