A coaxial cable has an inner conductor with radius r1 and current I going into the wire. The outer conductor has inner radius r2, outer radius r3 and the same current I going out of the wire. Both currents are evenly distributed through the cross section of the conductors.

a. Find expressions for the magnetic field within the inner conductor?
b. Find expressions for the magnetic field in the space between the conductors?
c. Find expressions for the magnetic field outside the outer conductor?

Answer with Explanation:

We are given that

Inner radius of outer conductor=

Outer radius of outer conductor=

Radius of inner conductor=

Current=I

a.Consider a loop of radius r<r1 Then, the current in the loop

Magnetic field withing the inner conductor,B=

b.Consider the loop of radius r where

Then, I'=I

c.Consider a loop of radius r

There is no current therefore,

B=0

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it