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5 March, 00:20

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.

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  1. 5 March, 00:44
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    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
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