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19 January, 00:11

An elastic conducting material is stretched into a circular loop of 14.7 cm radius. It is placed with its plane perpendicular to a uniform 0.963 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 74.5 cm/s. What emf is induced in volts in the loop at that instant?

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  1. 19 January, 00:21
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    Answer: 0.66 V

    Explanation:

    Given

    Magnetic field, B = 0.963 T

    Instantaneous rare = 74.5 cm/s = 0.745 m/s

    radius, r = 14.7 cm = 0.147 m

    We will use the formula

    emf = dΦ/dt

    emf = d (BA) / dt

    emf = d (Bπr²) / dt

    if B is constant, then we can say

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

    emf = Bπ (2r dr/dt)

    emf = 2πrB dr/dt substituting each values, we have

    emf = 2 * 3.142 * 0.147 * 0.963 * 0.745

    emf = 0.66 V

    Therefore, the induced emf in the loop at that instant is 0.66 V
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