Question

The diameter of the central wire in a very long triple conductor coaxial cable is

4.00 . Concentric around the wire is a middle cylindrical conductor with a diameter

of 2.60 and an outer conductor with a diameter of 5.00 . At some instant, the

wire carries a charge density of +15.0 /, the middle conductor carries a charge

density of −7.0 /, and the outer conductor carries a charge density of

−8.0 /. Derive expressions for the electric field as a function of radial distance in

each of the following regions: (a) between the wire and the central conductor (b)

between the middle and outer conductors (c) outside the outer conductor

Answer 1

Answer:

A coaxial cable consists of a long cylindrical copper wire of radius r1 surrounded by a cylindrical shell of inner radius r2 and outer radius r3 . The wire and the shell carry

equal and opposite currents I uniformly distributed over their volumes.

The magnetic field lines are circles, centered on the symmetry axis of the coaxial cable.

Consider an integration path with r >r3.

The path integral of B along this path is equal to

∫

B

.

dl

=2πrB=μ

0

I

The current enclosed by an integration path with a radius r > r3 is equal to zero (since the current in the wire and in the shell are flowing in opposite directions). The magnetic field in this region is therefore also equal to zero.