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2 years ago

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A certain superconducting magnet in the form of a solenoid of length 0.56 m can generate a magnetic field of 6.5 T in its core w

hen its coils carry a current of 80 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.

1 answer:

Gnom [1K]2 years ago

6 0

Answer:

The value is $N =36203 \ turns$

Explanation:

From the question we are told that

The length of the solenoid is $l = 0.56 \ m$

The magnetic field is $B = 6.5 \ T$

The current is $I = 80 \ A$

The desired temperature is $T = 4.2 \ K$

Generally the magnetic field is mathematically represented as

$B = \frac{\mu_o * N * I }{L }$

=> $N = \frac{B * L }{\mu_o * I }$

Here $\mu_o$ is the permeability of free space with value

$\mu_o = 4\pi * 10^{-7} N/A^2$

So

$N = \frac{6.5 * 0.56 }{ 4\pi * 10^{-7} * 80 }$

=> $N =36203 \ turns$

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