Differential Gauss's Law & Coaxial Cable

[Nekoteko]

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

A_cylinder = 2πbl

V_cylinder = πa²l

ρ = Q/V

∇∙E = ρ/ϵ₀

Q_enc = ∫_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.

 

[E_M_C]

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.

 

[vela]

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.

 

[Nekoteko]

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. :)

 

[vela]

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?

 

[Nekoteko]

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.

 

[E_M_C]

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 :)