A coiaxial cable consists of two thin coaxial cylinders electrically connected at one end, an inner cylindrical conducting tube of radius a carrying a steady current l which is screened by an outer cylindrical conducting sheath of radius b which provides a return path. There is no dielectric medium present.
Use Ampere's theorem to derive the total magnetic energy stored in the space between the conductors, show that the inductance of a length l of the cable is
`L=(mu_(0)l)/(2pi)ln((b)/(a))`
In this cable (a = 5 mm, b = 10 mm, l = 1000 m) is now employed in a (resistanceless) LC circuit containing a capacitance C = 1000 `muF`, determine the period of oscillations (neglect the capacitance of the cable itself).

Explanation

2.33 ms