Question

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 when 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.

Answer 1

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

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

=>   $N =36203 \ turns$