A coaxial cable consists of alternating coaxial cylinders of conducting and insulating material. Coaxial cabling is the primary type of cabling used by the cable television industry and is also widely used for computer networks such as Ethernet, on account of its superior ability to transmit large volumes of electrical signal with minimum distortion. Like all other kinds of cables, however, coaxial cables also have some self-inductance that has undesirable effects, such as producing some distortion and heating.
Consider a long coaxial cable made of two coaxial cylindrical conductors that carry equal currents I in opposite directions. The inner cylinder is a small solid conductor of radius a. The outer cylinder is a thin-walled conductor of outer radius b, electrically insulated from the inner conductor.
Calculate the inductance per unit length L/l of this coaxial cable. ( L is the inductance of part of the cable and l is the length of that part.)
Due to what is known as the "skin effect", the current I flows down the (outer) surface of the inner conducting cylinder and back along the outer surface of the outer conducting cylinder. However, you may ignore the thickness of the outer cylinder.