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12 January, 06:34

A coil of 43 turns in the shape of a rectangle with width 5 cm and length 10 cm is dropped from a position where magnetic field is 0 T to a position where the field is 0.5 T and is directed perpendicular to the plane of the coil. The displacement occurs in a time of 0.431 s. Calculate the resulting average emf induced in the coil

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  1. 12 January, 06:42
    0
    Given that,

    Number of turns

    N = 43 turns

    Dimensions of rectangle

    Length L = 10cm = 0.1m

    Width W = 5cm = 0.05

    Then, area of rectangle

    A = L*W = 0.1 * 0.05 = 0.005m²

    Initial magnetic field

    Bi = 0T

    Final magnetic field

    Bf = 0.5T

    The displacement time

    ∆t = 0.431s

    Induce emf ε?

    EMF is given as

    ε = - NdΦ/dt

    Where magnetic flux

    Φ = BA

    Note A is constant

    Then,

    ε = - NdΦ/dt = - Nd (BA) / dt

    ε = - N•A•dB/dt

    ε = - N•A• (∆B/∆t)

    ε = - N•A• (Bf - Bi) / (∆t)

    ε = - 43 * 0.005 * (0.5 - 0) / 0.431

    ε = - 43 * 0.005 * 0.5 / 0.431

    ε = - 0.249 V

    The average induced EMF is 0.249V
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