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Question: The magnetic field at the surface of a long wire radius R and carrying a current I is 0I2R . How large acurrent could a 0.1 mm diameter niobium wire carry without exceeding its 0.2 T critical field?

Short Answer

Expert verified

Answer

Current in the wire is 50A.

Step by step solution

01

Given data

Diameter of niobium wire is, 0.1mm .

Maximum magnetic field is,0.2T .

02

 Step 2: Formula of Magnetic Field produced by a Wire

given by, B=0I2R .

Here I represents current, R represents radius of wire and0 represents permeability of free space.

03

Calculate the Current from the Expression of Magnetic Field produced by a Wire

The radius of the wire is, R=D2.

Substitute 0.1mmD and convert it into m .

R=D2=0.1mm2=0.05mm10-3m1mm=0.0510-3m

The magnetic field produced by the current is given by, B=0I2R.

Rearrange the above equation for l .

B=0I2R

Substitute 410-7Tm/A0,0.2TB, and 0.0510-3mR in the above equation.

B=0I2RI=2RB0=20.0510-3m(0.2T)410-7Tm/A=50A

Current in the wire is 50 A .

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