certain superconducting magnet in the form of a solenoid of length 0.34 m can generate a magnetic field of 6.5 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.

The number of turns in the solenoid is 1.95 x 10⁴.

Explanation:

given information:

the length of solenoid, L = 0.34 m

magnetic field, B = 6.5 T

current, I = 90 A

to find the number of turn in solenoid, we can start from the magnetic field equation,

B = μ₀nI, n = N/L

B = magnetic field (T)

μ₀ = permeability (4π * 10⁻⁷ T. m/A)

n = the number turn per unit length (turn/m)

I = current (A)

N = the number turn in solenoid

L = the length of solenoid

thus,

B = μ₀IN/L

N = B L/μ₀I

= (6.5) (0.34) / (4π * 10⁻⁷) (90)

= 1.95 x 10⁴ turn