Chapter 30, Problem 30.46P

CP CALC A Coaxial Cable. A small solid conductor with radius a is supported by insulating, nonmagnetic disks on the axis of a thin-walled tube with inner radius b. The inner and outer conductors carry equal currents i in opposite directions. (a) Use Ampere’ law to find the magnetic field at any point in the volume between the conductors. (b) Write the expression for the flux dФ_B through a narrow strip of length parallel to the axis, of width dr, at a distance r from the axis of the cable and lying in a plane containing the axis. (c)Integrate your expression from part (b) over the volume between the two conductors to find the total flux produced by a current i in the central conductor. (d) Show that the inductance of a length l of the cable is

$L=l\frac{{\mu }_0}{2\pi }\ln \left(\frac{b}{a}\right)$

(e) Use Eq. (30.9) to calculate the energy stored in the magnetic field for a length l of the cable.