- #1
WitnessJah
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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
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