A long coaxial cable, above, consists of a solid cylindrical conductor of radius

Question

A long coaxial cable, above, consists of a solid cylindrical conductor of radius a, surrounded by a hollow coaxial conductor of inner radius b and outer radius c. The two conductors carry uniformly distributed current but in opposite directions. The current is to the right in the outer cylinder and to the left in the inner cylinder. Use Amperes law to determine the magnitude of the magnetic field at a distance r from the axis of the cable in each of the following cases:

i. 0<r<a                     ii. a<r<b

Explanation / Answer

i. Use ?B•ds=µI, and I/Io = pr2/pa2 to get B = (µoIr)/(2pa2) ii. Use Ampere’s Law to get B=(µoI)/(2pr)

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