- #1
thecommexokid
- 70
- 2
Homework Statement
A long coaxial cable carries current I. The current flows down the surface of the inner cylinder (of radius a) and back along the outer cylinder (of radius b). Calculate the power transported down the wire.
Homework Equations
The Poynting vector is given by [itex]\mathbf{S} = \frac{1}{\mu_0}\mathbf{E}\times\mathbf{B}[/itex]. From there I should have no trouble finishing off the problem.
The Attempt at a Solution
I found the magnetic field no problem with Ampère's law. It is [itex]\mathbf{B}(s) = \frac{\mu_0I}{2\pi s}\hat{\boldsymbol{\phi}}[/itex] for a < s < b and B(s) = 0 otherwise.
My trouble is with finding the electric field. There are two possible sources of electric fields. One is time-varying magnetic fields. But the magnetic field here is time-independent. The second is static charges. But both the inner and outer cylinder are electrically neutral overall. (Their positive charges happen to be stationary while their negative charges are in motion, but they still should have equal amounts of each.) So by my calculations, E = 0.
But that would mean no Poynting vector, and that would mean no power, and that's probably not the answer to this question.