A coaxial cable consists of two very thin-walled conducting cylinders of radii r1 and r2 (Figure). Current I goes in one direction down the inner cylinder and in the opposite direction in the outer cylinder.
-1.PNG "A coaxial cable consists of two very thin-walled conducting cyli 1")
(a) Use Ampere’s law to find B. Show that B = 0 except in the region between the conductors.
(b) Show that the magnetic energy density in the region between the cylinders is
-2.PNG "A coaxial cable consists of two very thin-walled conducting cyli 2")
(c) Find the magnetic energy in a cylindrical shell volume element of length ℓ and volume dV = ℓ2πr dr, and integrate your result to show that the total magnetic energy in the volume of length ℓ is
-3.PNG "A coaxial cable consists of two very thin-walled conducting cyli 3")
(d) Use the result in part (c) and Um = ½LI2 to show that the self-inductance per unit length is
-4.PNG "A coaxial cable consists of two very thin-walled conducting cyli 4")
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