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Differential Gauss's Law & Coaxial Cable

  • Thread starter Nekoteko
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  • #1
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Homework Statement



A long coaxial cable consists of an inner solid cylinder, radius a, and an outer thin coaxial cylindrical shell, radius b. The outer shell carries a uniform surface charge density σ.
Find the uniform volume charge density ρ that the inner cylinder must have in order that the whole cable (inner + outer) is neutral.

Homework Equations


Acylinder = 2πbl

Vcylinder = πa2l

ρ = Q/V

∇∙E = ρ/ϵ0

Qenc = ∫Vρdτ

The Attempt at a Solution


I feel like I have all the relevant equations, yet, I still do not know how to start this. Any hints? Very much appreciated.
 

Answers and Replies

  • #2
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Hi Nekoteko,

The problem is asking you to find ρ such that the total charge in the inner cylinder is equal to the total charge on the outer cylinder.

Another way of saying this is: For what ρ does the electric field in the region outside of both cylinders equal zero?

Try using Gauss' Law to find the electric field in the region outside of both cylinders.
 
  • #3
vela
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This is a very basic review problem for an upper-division electromagnetics course. If you have no idea how to start this, you must not have tried very hard. You need to show a decent effort before you receive help here.
 
  • #4
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lol Is there a reason you're so reluctant to help?

E_M_C, that's really all the hint I needed! It's so simple, not sure why I didn't see that yesterday. Thanks. :)
 
  • #5
vela
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lol Is there a reason you're so reluctant to help?
Yes, read the forum rules, the ones you agreed to when you registered here. Did you really need a hint to understand what the word neutral meant?
 
  • #6
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Lol I didn't ask for help to piss you off. What do you want me to do if I can't figure something out myself? I understand the forum rules, but if I needed help, I needed help, I don't care how stupid you think my question was (it was). Besides, not like I was asking anybody to solve it for me, just a hint is all I needed. And neutral isn't the problem I had w/ this question. Relax your internet authority, lol.
 
  • #7
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This is a very basic review problem for an upper-division electromagnetics course. If you have no idea how to start this, you must not have tried very hard. You need to show a decent effort before you receive help here.
There's no need for that kind of behavior.

E_M_C, that's really all the hint I needed! It's so simple, not sure why I didn't see that yesterday. Thanks. :)
You're very welcome :)
 

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