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A certain superconducting magnet in the form of a solenoid of length 0.24 m can generate a magnetic field of 7.0 T in its core when its coils carry a current of 90 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.

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Khoso123

Answer:

[tex]N=14854.5turns[/tex]

Explanation:

Given data

Length L=0.24 m

Magnetic field B=7.0 T

Current I=90 A

To find

Number of turns N

Solution

As we know that magnetic field is given as:

[tex]B=u_{o}I\frac{N}{L}[/tex]

Rearrange the equation and solve for N

So

[tex]B=u_{o}I\frac{N}{L}\\\frac{B}{u_{o}I} =\frac{N}{L} \\N=\frac{LB}{u_{o}I}\\N=\frac{(0.24m)(7.0T)}{4\pi *10^{-7}*(90A)} \\N=14854.5turns[/tex]

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