A. A long straight cable with radius R carries a current uniformly distributed through its circular cross section. Find the self-inductance per unit length of the cable. Hint: find B inside and outside, then find energy everywhere and relate to the self-inductance (per unit length)
B. This cable is now modified to have an insulator wrapped around it and another thin conductor wrapped around the surface of the outer conductor. Find the self-inductance (per unit length) of the cable now.
C. Find the self inductance per unit length on a hollow cable where the current only runs on the surface of the outer conductor.
Show all calculations and explain the process involved in each step.
This solution provides step-by-step processes for the calculations of magnetic self-inductance of a long coaxial cable, including final values. Each calculation is also accompanied by a clear written explanation that describes the scientific premise the calculations are based on. Three cases of radial structure of a cable are considered.