Finding the surface charge density

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SUMMARY

The surface charge density of a 1.0-mm-diameter wire with 1000 excess electrons per centimeter of length is calculated to be 5.1 x 10^-12 C/m². The formula used is η = Q/A, where Q is the total charge and A is the surface area of the cylindrical wire. The correct surface area is determined by the formula SA = 2πrh, where r is the radius and h is the length of the wire segment. The calculation confirms that only the outer surface area is relevant for determining the surface charge density, as the ends of the wire do not contribute to the charge in this context.

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  • Understanding of surface charge density and its significance in electrostatics
  • Familiarity with cylindrical geometry and surface area calculations
  • Basic knowledge of charge quantization and electron properties
  • Proficiency in using fundamental equations in electrostatics, specifically η = Q/A
NEXT STEPS
  • Study the derivation and applications of the formula for surface charge density in various geometries
  • Explore the concept of electric fields around charged cylindrical objects
  • Learn about the implications of charge distribution on the behavior of conductors
  • Investigate the relationship between surface charge density and capacitance in cylindrical capacitors
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Students in physics, particularly those studying electromagnetism, electrical engineers, and anyone interested in understanding charge distribution in conductive materials.

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

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