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A coaxial cable consists of two thin coaxial cylinders electrically connected at one end; an inner cylindrical conducting tube of radius a carrying a steady current I which is screened by an outer cylindrical conducting sheath of radius b which provides a return path. There is no dielectric medium present.
Using Ampere’s theorem to derive the total magnetic energy stored in the space between the conductors, show that the inductance of a length I of the cable is
L = μ0I/2π In (b/a).
If this cable (a = 5 mm, b = 10 mm, l = 1000m) is now employed in a (resistanceless) LC circuit containing a capacitance C = 1000 μF, determine the period of oscillations (neglect the capacitance of the cable itself).
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