The element niobium, which is a metal, is a superconductor at temperatures below

Question

The element niobium, which is a metal, is a superconductor at temperatures below 9 K . This means that at such low temperatures a niobium wire has no electrical resistance. The superconductivity of the wire, however, is destroyed if the magnetic field at the surface of the wire exceeds 0.10 T . What is the maximum current in a straight superconducting niobium wire of radius 1.5 mm ? You may assume that all the current flows in the center of the wire.

Create a visual representation of the problem. First choose the best orientation for the wire, then draw the magnetic field created by the current. You can then determine your known variables and identify those that you must find.

Part A

What is the most convenient way to represent the niobium wire in your figure?

E) out of the plane of the paper, but not perpendicular to it

A ) in the plane of the paper with the current flowing horizontally B) in the plane of the paper with the current flowing vertically C) in the plane of the paper with the current flowing neither horizontally nor vertically D) perpendicular to the plane of the paper with the current flowing either into or out of the paper

E) out of the plane of the paper, but not perpendicular to it

Explanation / Answer

B = 0.10 T , r = 1.5 mm = 0.0015 m

I = 2 B r / µ0

I = 2 B d / 4 X 10-7

I = 2 X X 0.10 X 0.0015 / 4 X 10-7

I = 7.5 X 10-5 / 10-7

I = 7.5 X 102

I = 750 A

Part A :

D)

perpendicular to the plane of the paper

with the current flowing either into or out of the paper .

assumed all the current flows in the center of the wire

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