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25 March, 16:03

A square loop of wire is held in a uniform 0.24 T magnetic field directed perpendicular to the plane of the loop. The length of each side of the square is decreasing at a constant rate of 5.4 cm/s. What emf is induced in the loop when the length is 14 cm?

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  1. 25 March, 19:55
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    Given that,

    Magnetic field of 0.24T

    B = 0.24T

    Field perpendicular to plane i. e 90°

    Rate of decrease of length of side of square is 5.4cm/s

    dL/dt = 5.4cm/s = 0.054m/s

    Since it is decreasing

    Then, dL/dt = - 0.054m/s

    When L is 14cm, what is the EMF induced?

    L = 14cm = 0.14m

    EMF is give as

    ε = - dΦ/dt

    Where flux is given as

    Φ = BA

    Where A is the area of the square

    A = L²

    Then, Φ = BL²

    Substituting this into the EMF

    ε = - dΦ/dt

    ε = - d (BL²) / dt

    B is constant

    ε = - Bd (L²) / dt

    ε = - 2BL dL/dr

    ε = - 2 * 0.24 * 0.14 * - 0.054

    ε = 3.63 * 10^-3 V

    ε = 3.63mV
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