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29 October, 08:52

A flat, 193 193 ‑turn, current‑carrying loop is immersed in a uniform magnetic field. The area of the loop is 4.55 cm 2 4.55 cm2 and the angle between its magnetic dipole moment and the field is 59.1 ∘. 59.1∘. Find the strength B B of the magnetic field that causes a torque of 1.47 * 10 - 5 N ⋅ m 1.47*10-5 N⋅m to act on the loop when a current of 2.13 mA 2.13 mA flows in it.

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Answers (2)
  1. 29 October, 10:25
    0
    Given Information:

    Torque = τ = 1.47*10⁻⁵ N. m

    Current = I = 2.13 mA = 0.00213 A

    Number of turns = N = 193

    Angle = θ = 59.1°

    Area = A = 4.55 cm² = 0.000455 m²

    Required Information:

    Magnetic field = B = ?

    Answer:

    Magnetic field = 9.159*10⁻² T

    Explanation:

    The toque τ is given by

    τ = NIABsin (θ)

    B = τ/NIAsin (θ)

    Where N is the number of turns, I is the current flowing through the loop, A is the area of flat loop and θ is angle between magnetic dipole moment and magnetic field B,

    B = 1.47*10⁻⁵ / (193*0.00213*0.000455*sin (59.1))

    B = 9.159*10⁻² T

    Therefore, the strength of the magnetic field is 9.159*10⁻² T.
  2. 29 October, 12:00
    0
    0.0916 T

    Explanation:

    Parameters given:

    Number of turns, N = 193

    Area of loop, A = 4.55cm² = 0.000455 m²

    Angle, θ = 59.1°

    Torque, τ = 1.47 * 10^ (-5) Nm

    Current, I = 2.13 mA = 0.00213 A

    Using the formula for torque, we can find the magnetic field, B:

    τ = N * I * A * B * sinθ

    => B = τ / (N * I * A * sinθ)

    B = (1.47 * 10^ (-5)) / (193 * 2.13 * 10^ (-3) * 0.000455 * sin59. 1)

    B = 0.0916 T
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