A long solenoid that has 1,030 turns uniformly distributed over a length of 0.37

Question

A long solenoid that has 1,030 turns uniformly distributed over a length of 0.370 m produces a magnetic field of magnitude 1.00 Times 10^-4 T at its center. What current is required in the windings for that to occur? A certain superconducting magnet in the form of a solenoid of length 0.30 m can generate a magnetic field of 13.0 T in its core when its coils carry a current of 100 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.

Explanation / Answer

1)

Using this equation:
B = 0 x N/L x I
B = 1.00 x 10-4 T
0 = 1.26 x 10-6
N/L = 1030 turns/0.370 m =2783.78 turns/meter

B = 0 x N/L x I
I = B / ( 0 x N/L)
I = 1.00 x 10-4 T / (1.26 x 10-6)(2783.78 turns/meter)
= 2.85x 10-02 A

2)

B = µNI/h

B is the magnetic field in teslas

h is length of solenoid in meters

N is number of turns

I is current in amps

µ is the magnetic constant

B = µNI/h

13 =1.26 x 10-6*N*100/0.30

N=32500 turns

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