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13 December, 00:06

An eight-turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm. The coil lies in the plane of the page and carries a clockwise current of 6.20 A. If the coil is in a uniform magnetic field of 1.98 10-4 T directed toward the left of the page, what is the magnitude of the torque on the coil? Hint: The area of an ellipse is A = ? ab, where a and b are, respectively, the semimajor and semiminor axes of the ellipse.

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  1. 13 December, 01:44
    0
    9.25 x 10^-4 Nm

    Explanation:

    number of turns, N = 8

    major axis = 40 cm

    semi major axis, a = 20 cm = 0.2 m

    minor axis = 30 cm

    semi minor axis, b = 15 cm = 0.15 m

    current, i = 6.2 A

    Magnetic field, B = 1.98 x 10^-4 T

    Angle between the normal and the magnetic field is 90°.

    Torque is given by

    τ = N i A B SinФ

    Where, A be the area of the coil.

    Area of ellipse, A = π ab = 3.14 x 0.20 x 0.15 = 0.0942 m²

    τ = 8 x 6.20 x 0.0942 x 1.98 x 10^-4 x Sin 90°

    τ = 9.25 x 10^-4 Nm

    thus, the torque is 9.25 x 10^-4 Nm.
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