Coaxial Cable Problem - Finding volume charge density.

  • Thread starter WitnessJah
  • Start date
  • #1
1. 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.

2. Homework Equations

Acylinder = 2πbl

Vcylinder = πa^2l

Qenc = ∫Vρdτ

3. The Attempt at a Solution


I started by using dq = sigma*dS, and integrating to get Q_b = -2(pi)(sigma)bL. That should be the total charge on the outer cylindrical shell.

Then I set -Q_b = Q_a, so the net charge of the entire system would be equal to 0.

Next I used Q_a = row*integral(dVolume) = -Q_b

to get to (row)(pi)(a^2)(L) = 2(pi)(sigma)(b)(L)

Solving for row gave me:

row = [2(sigma)(b)] / a^2


Does this look like a proper method and correct solution?

Thank you so much for your time.

WJ
 

Answers and Replies

  • #2
35,389
11,734
That looks right.
 

Related Threads on Coaxial Cable Problem - Finding volume charge density.

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
11
Views
6K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
1
Views
8K
Replies
1
Views
1K
Replies
5
Views
1K
Top