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8 September, 11:30

A circular coil of 185 turns has a radius of 1.60 cm. (a) Calculate the current that results in a magnetic dipole moment of magnitude 1.79 A·m2. (b) Find the maximum magnitude of the torque that the coil, carrying this current, can experience in a uniform 47.7 mT magnetic field.

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  1. 8 September, 13:26
    0
    Given Information:

    Number of turns = N = 185 turns

    Radius of circular coil = r = 1.60 cm = 0.0160 m

    Magnetic field = B = 47.7 mT

    Magnetic dipole moment = µ = 1.79 A. m

    Required Information:

    (a) Current = I = ?

    (b) Maximum Torque = τ = ?

    Answer:

    (a) Current = 12.03 A

    (b) Maximum Torque = 0.0853 N. m

    Explanation:

    (a) The magnetic dipole moment µ is given by

    µ = NIAsin (θ)

    I = µ/NAsin (θ)

    Where µ is the magnetic dipole moment, N is the number of turns, I is the current flowing through the circular loop, A is the area of circular loop and is given by

    A = πr²

    A = π (0.0160) ²

    A = 0.000804 m²

    I = 1.79/185*0.000804*sin (90)

    I = 12.03 A

    (b) The toque τ is given by

    τ = NIABsin (θ)

    The maximum torque occurs at θ = 90°

    τ = 185*12.03*0.00804*0.0477*sin (90°)

    τ = 0.0853 N. m
  2. 8 September, 14:15
    0
    (a) the current in the coil is 12.03 A

    (b) the maximum magnitude of the torque is 0.0854 N. m

    Explanation:

    Given;

    number of turns, N = 185

    radius of the coil, r = 1.6 cm = 0.016 m

    magnetic dipole moment, μ = 1.79 A·m²

    Part (a) current in the coil

    μ = NIA

    Where;

    I is the current in the coil

    A is the of the coil = πr² = π (0.016) ² = 0.000804 m²

    I = μ / (NA)

    I = 1.79 / (185 x 0.000804)

    I = 1.79 / 0.14874

    I = 12.03 A

    Part (b) the maximum magnitude of the torque

    τ = μB

    Where;

    τ is the maximum magnitude of the torque

    B is the magnetic field strength = 47.7 mT

    τ = 1.79 x 0.0477 = 0.0854 N. m
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