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19 April, 22:23

A single-turn loop of wire has a resistance of 6.00 Ω and a cross-sectional area 300 cm2 and is perpendicular to a uniform magnetic field which increases at a constant rate from 0.200 T to 3.60 T in 0.500 seconds. What is the magnitude of the induced current in the loop?

A. 0.34 AB. 34 mAC. 2.04 AD. 36 mAE. 0.36 A

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  1. 19 April, 23:19
    0
    Given that,

    Resistance of wire

    R = 6.00 Ω

    Cross sectional area

    A = 300cm² = 0.03m²

    Initial magnetic field Bi = 0.2T

    Final magnetic field Bf = 3.6T

    Time taken t = 0.5s

    Current?

    From ohms law

    V=iR

    Then, I = V/R

    Therefore, we need to find the induced EMF in the coil

    ε = - dΦ/dt

    Where Φ = BA

    Where the Area is constant

    ε = - dΦ/dt = - d (BA) / dt

    Since A is constant

    ε = - A•dB/dt

    ε = - A• (∆B) / ∆t

    ε = - 0.03 (3.6-0.2) / 0.5

    ε = - 0.204 V

    Then, the magnitude of the EMF is 0.204 V

    So,

    I = V/R

    I = 0.204/6

    I = 0.034 Amps

    I = 34 mA

    Option B is correct.
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