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A certain superconducting magnet in the form of a solenoid of length 0.56 m can

ID: 1492043 • Letter: A

Question

A certain superconducting magnet in the form of a solenoid of length 0.56 m can generate a magnetic field of 4.0 T in its core when its coils carry a current of 95A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.
turns
A certain superconducting magnet in the form of a solenoid of length 0.56 m can generate a magnetic field of 4.0 T in its core when its coils carry a current of 95A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.
turns

Explanation / Answer

The number of turns in the solenoid can be calculated using following formula:

B = µ0*N*I / h

Where µ0 = magnetic constant = 1.2566*10^-6 H/m

N = number of turns required over here

I = current in amperes = 95 A

h = length of solenoid in meters = 0.56 m

B = magnetic field in teslas = 4 T

Putting all these values in the main equation mentioned at the top,

4 = (1.2566*10^-6)*N*(95) / (0.56)

=> No of turns in the solenoid = N  = 18764 turns

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