Question

A certain superconducting magnet in the form of a solenoid of length 0.26 m can generate a magnetic field of 7.5 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:

Therefore

Number of turns in the solenoid is 19407.

Explanation:

Given:

Strength magnetic field at its center,

B = 7.5 T

length of solenoid = l = 0.26 m

Current, I = 80 A

To Find:

Turn = N = ?

Solution:

If N is the number of turns in the length, the total current through the rectangle is NI. Therefore, Ampere’s law applied to this path gives

$\int {B} \, ds= Bl=\mu_{0}NI$

Therefore,

$B =\dfrac{\mu_{0}NI}{l}$

Where,  

B = Strength of magnetic field

l = Length of solenoid

N = Number of turns

I = Current

$\mu_{0}=Permeability\ in\ free\ space=4\pi\times 10^{-7}\ Tm/A$

$N=\dfrac{Bl}{\mu_{0}I}$

Substituting the values we get

$N=\dfrac{7.5\times 0.26}{4\pi\times 10^{-7}\times 80}=19406.84=19407$

Therefore

Number of turns in the solenoid is 19407.