An elastic conducting material is stretched into a circular loop of 14.8 cm radius. It is placed with its plane perpendicular to a uniform 0

Question

An elastic conducting material is stretched into a circular loop of 14.8 cm radius. It is placed with its plane perpendicular to a uniform 0.814 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 88.4 cm/s. What emf is induced in volts in the loop at that instant

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Dulcie 4 years 2021-08-03T10:08:28+00:00 1 Answers 13 views 0

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  1. Vodka
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    2021-08-03T10:10:17+00:00
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    Answer: 0.666 V

    Explanation:

    Given

    Radius of the loop, r = 14.8 cm = 0.148 m

    Magnetic field present, B = 0.814 T

    Rate of shrinking, dr/dt = 88.4 cm/s = 0.884 m/s

    emf = dΦ/dt , where Φ = BA

    emf = d(BA)/dt, where A = πr²

    emf = d(Bπr²)/dt

    if B is constant, then

    emf = Bπ d(r²)/dt, on differentiating, we have,

    emf = Bπ * 2r dr/dt

    emf = 2πrB dr/dt, now if we substitute the values, we have

    emf = 2 * 3.142 * 0.148 * 0.814 * 0.884

    emf = 6.284 * 0.106

    emf = 0.666 V

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