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19 August, 13:03

A circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.069 T. The plane of the loop is perpendicular to the direction of the magnetic field. In a time interval of 0.40 s, the magnetic field changes to the opposite direction with a magnitude of 0.043 T. What is the magnitude of the average emf induced in the loop?

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  1. 19 August, 13:06
    0
    0.33 mV or 0.00033 V

    Explanation:

    Parameters given:

    Radius, r = 4 cm = 0.04 m

    Number of turns, N = 1

    Initial magnetic field, Bini = 0.069 T

    Final magnetic field, Bfin = 0.043 T

    Time, t = 0.4 secs

    EMF induced in a coil is given as the time rate of change of Magnetic Flux:

    EMF = - ΔΦ/t

    ΔΦ = ΔB * A

    Where ΔB = change in magnetic field

    A = area = pi * r²

    EMF = - [ (Bfin - Bini) * N * pi * r²] / t

    EMF = - [ (0.043 - 0.069) * 1 * 3.142 * 0.04²] / 0.4

    EMF = 0.00033 V = 0.33 mV
  2. 19 August, 13:22
    0
    Given Information:

    Radius of circular loop = r = 4 cm = 0.04 m

    Initial Magnetic field = B₁ = 0.069 T

    Final Magnetic field = B₂ = 0.043 T

    time interval = Δt = 0.40 seconds

    Required Information:

    Average induced emf = ξ = ?

    Answer:

    Average induced emf = 3.26x10⁻⁴ V

    Explanation:

    The induced EMF ξ is given by

    ξ = - NΔΦ/Δt

    Where change in flux ΔΦ can be found using

    ΔΦ = (B₂ - B₁) A

    Area is given by

    A = πr²

    A = π (0.04) ²

    A = 0.005026 m²

    ΔΦ = (0.043 - 0.069) * 0.005026

    ΔΦ = - 0.0001306 T. m²

    So the average induced emf is

    Assuming number of turns N = 1

    ξ = - NΔΦ/Δt

    ξ = - 1 * (-0.0001306) / 0.40

    ξ = 0.0003265 V

    ξ = 3.26x10⁻⁴ V
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