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

The value is
`N =36203 \ turns`

Step-by-step 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 = (\mu_o * N * I )/(L )`

=>
`N = (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 = (6.5 * 0.56 )/( 4\pi * 10^(-7) * 80 )`

=>
`N =36203 \ turns`