Consider the coaxial cable of Problem 30.48. The conductors carry equal currems i in opposite directions.
(a) Use Ampere's law to find the magnetic field at any point in the volume between the conductors.
(b) Use the energy density for a magnetic field, Eq. (30.10), to calculate the energy stored in a thin, cylindrical shell between the two conductors. Let the cylindrical shell have inner radius r, outer radius r + dr, and length l.
(c) integrate your result in part (b) over the volume between the two conductors to find the total energy stored in the magnetic field for a length 1 of the cable.
(d) Use your result in part (c) and Eq. (30.9) to calculate the inductance L of a length l of the cable. Compare your result to L calculated in part (d) of Problem 30.48.