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$$s law to find the magnetic field at any point in the volume between the conductors. $($b$)$ Write the expression for the flux d$$B through a narrow strip of length l 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 m$02$p lna b a b $($e$)$ Use Eq$.(30\mathrm{.}9)$ to calculate the energy stored in the magnetic field for a length l of the cable