Find the magnetic-energy density as a function of radial distance for the coaxial cable of Problem 72, and integrate over the volume between the conductors to show that the total energy per unit length of the cable is given by (?₀I²/4?)ln(b/a) Use the expression U = 1/2LI² to find the inductance per unit length, and show that your result agrees with that of Problem 72.

Data From Problem 72

A long, straight coaxial cable consists of two thin, tubular conductors, the inner of radius a and the outer of radius b. Current I flows out along one conductor and back along the other. Show that the self-inductance per unit length of the cable is ?.

Transcribed Image Text:

- In (bla)