Coaxial cable
A coaxial cable consists of an inner solid cylindrical wire of radius and an outer conducting hollow cylinder of radius , which each carry a current of magnitude . If the currents travel in opposite directions, what is the magnitude of the magnetic field outside of the cable a distance of measured perpendicularly from the central axis of the inner wire?
The answer is 0.
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1 solution
The total current enclosed inside a circular Amperian loop centered at the central axis of the inner wire is zero. Due to the symmetry of the problem, Ampère's law concludes that the magnetic field at any point on the loop is zero.