Finding the surface charge density

In summary, the problem involves calculating the surface charge density of a 1.0-mm-diameter wire with 1000 excess electrons per centimeter of length. The surface charge density is found by dividing the charge by the surface area, which only includes the outer surface of the wire. This results in a surface charge density of 5.1 * 10^-12 C/m^2.
  • #1
jheld
81
0

Homework Statement


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


Homework Equations


[tex]\eta[/tex] = Q/A


The Attempt at a Solution


[tex]\eta[/tex] = (100000 * 1.6*10^-19)/([tex]\pi[/tex] * (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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  • #2
What's the surface area (not the cross-sectional area) of that section of wire?
 
  • #3
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
jheld said:
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.
 
  • #5
Okay.
eta = 10 * 1.6*10^-19 C/(2pi * (5 * 10^-4 m) * (10^-3 m)) = 5.1 * 10^-12 C/m^2
That's the right answer :)
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
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
Yeah, thanks that really helped. Thanks for the help :)
 

Related to Finding the surface charge density

1. What is surface charge density?

Surface charge density is a measure of the amount of electric charge per unit area on a surface. It is represented by the symbol σ and is typically measured in coulombs per square meter (C/m²).

2. How do you calculate surface charge density?

To calculate surface charge density, divide the total electric charge on a surface by the surface area. The equation is σ = Q/A, where σ is the surface charge density, Q is the total charge, and A is the surface area.

3. What is the importance of finding surface charge density?

Finding the surface charge density is important in understanding the behavior of electric fields and how they interact with charged surfaces. It also plays a crucial role in various applications, such as in the design of electronic devices and in studying the properties of materials.

4. How is surface charge density measured?

Surface charge density can be measured using several methods, including using a coulomb meter, an electrostatic voltmeter, or by indirect methods such as measuring the force between two charged plates or the deflection of a charged object in an electric field.

5. How does surface charge density affect the electric field?

Surface charge density has a direct relationship with the electric field strength. The higher the surface charge density, the stronger the electric field will be at that surface. This is because the electric field is directly proportional to the charge density.

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