"A coaxial cable consists of an inner wire and a concentric cylindrical outer conductor. If the conductors carry equal but opposite charges, show that there is no net charge on the outside of the outer conductor.
The Attempt at a Solution
I tried to approach this problem as logically as possible before laying any numbers to paper or manipulating equations, but was not able to even get that far. Our teacher brushed over very quickly the concept of uniform volume charge distribution and conductors in electric fields. I know there can be no electric field within a conductor. Therefore, if we assume the wire carries a negative charge, then that means there is an excess of electrons that will move themselves to the surface of the conductor, correct? ("If a conductor in electrostatic equilibrium carries a net charge, it must reside on the conductor surface"). So we have a negative field resulting in the cavity thus far. However, if we assume the outside cylindrical shell to be positive in charge, then there will be a positive net charge on the surface of the shell, both on the inside by the wire and the outside as well, correct? Now because of uniform charge distribution, the charge on the inside of the shell will in effect cancel its own field out, still leaving a negative field inside the cavity, but how is the net charge on the outside of the shell in any way negated by the wire? It has to have a positive net charge according to Gauss's law? Thanks for any tips, suggestions or hints!