Finding the surface charge density

1. Mar 10, 2009

jheld

1. The problem statement, all variables and given/known data
A 1.0-mm-diameter wire has 1000 excess electrons per centimeter of length. What is the surface charge density?

2. Relevant equations
$$\eta$$ = Q/A

3. 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?

2. Mar 10, 2009

Staff: Mentor

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

3. Mar 10, 2009

jheld

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.

4. Mar 10, 2009

Staff: Mentor

Don't include the circular end pieces, just the outer surface.

The height corresponds to the length.

5. Mar 10, 2009

jheld

Okay.
eta = 10 * 1.6*10^-19 C/(2pi * (5 * 10^-4 m) * (10^-3 m)) = 5.1 * 10^-12 C/m^2
But, I'm a little confused as to why I only take the area of the outer surface and not the end pieces as well? Is that because I'm only concerned with one "portion" of the wire, and I'm therefore only calculating a piece and not the whole thing?

6. Mar 10, 2009

Staff: Mentor

Note that you're given the charge per centimeter, which only sits on the outside of the wire. Think of the wire as being very long and that you are just looking at a typical one cm section somewhere in the middle. The "ends" of that section have no charge--only the outside counts. Make sense?

7. Mar 10, 2009

jheld

Yeah, thanks that really helped. Thanks for the help :)