An electrical current flow without any resistance in a superconductor along its

Question

An electrical current flow without any resistance in a superconductor along its surface. If we think of a particular superconducting wire as an infinitely long, straight cylinder of radius 3 cm. Then the current only flows along the surface of this cylinder (no current flows in the interior of the wire). Use Ampere's law to determine the following when the superconducting wire carries a 3.5 A current. What is the magnitude of the magnetic field inside the wire a distance 1 cm from its center? What is the magnitude of the magnetic field outside the wire a distance 7 cm from its center?

Explanation / Answer

a)The magnetic field inside the wire is given by

B = u0 I r / 2 pi R

where u0, is the permeability of free space, I is the current, r is the distance wrt to axis, R is the radius

B = 4 pi x 10^-7 x 3.5 x 0.01/ 2 pi x 0.03^2 = 7.78 x 10^-6 T

Hence, B = 7.78 x 10^-6 T

b)B field outside the wire at r = 7 cm = 0.07 will be:

B = u0 I/ 2 pi r

B = 4 pi x 10^-7 x 3.5 / 2 pi x 0.07 = 1 x 10^-5 T

Hence, B = 1 x 10^-5 T

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