A 119 turn119 turn circular coil of radius 2.47 cm2.47 cm is immersed in a uniform magnetic field that is perpendicular to the plane of the

Question

A 119 turn119 turn circular coil of radius 2.47 cm2.47 cm is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. Over an interval of 0.167 s0.167 s , the magnetic field strength increases from 57.9 mT57.9 mT to 96.9 mT96.9 mT . Find the magnitude of the average emf avgEavg induced in the coil during this time interval, in millivolts.

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Mít Mít 3 years 2021-07-24T05:17:53+00:00 1 Answers 11 views 0

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  1. MichaelMet
    0
    2021-07-24T05:18:55+00:00
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    Answer:

    Explanation:

    Given that,

    Number of turns is 119

    N = 119

    The radius of the coils is 2.47 cm

    R = 2.47 cm = 0.0247m

    Then, the area of the circular coil is given as

    A = πr²

    A = π × 0.0247²

    A = 1.917 × 10^-3 m²

    Time interval

    t = 0.167s

    The magnetic field strength increases from B1 = 57.9mT to B2 = 96.9 mT

    Then,

    ∆B = B2 – B1 = 96.9 — 57.9 = 39 mT

    ∆B = 39 × 10^-3 T

    We want find the average emf

    EMF induced in a coil is given as

    ε = -N dΦ / dt

    Then, magnetic flux (Φ) is given as

    Φ = BA

    Then,

    ε = -N dΦ / dt

    ε = -N d(BA) / dt

    Since the area is constant, so we have

    ε = -N•A dB / dt

    ε = -N •A • ∆B / ∆t

    So, inserting the parameters above

    ε = – 199 × 1.917 × 10^-3 × 39 × 10^-3 / 0.167

    ε = 0.0891 V

    To mV

    ε = 89.1 × 10^-3 V

    ε = -89.1 mV

    Then, the magnitude of EMF induced in the coil is 89.1 mV

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