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19 December, 07:51

A wire loop of radius 0.50 m lies so that an external magnetic field of magnitude 0.40 T is perpendicular to the loop. The field reverses its direction, and its magnitude changes to 0.20 T in 2.5 s. Find the magnitude of the average induced emf in the loop during this time.

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  1. 19 December, 08:55
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    The magnitude of the induced emf is given by:

    ℰ = |Δφ/Δt|

    ℰ = emf, Δφ = change in magnetic flux, Δt = elapsed time

    The magnetic field is perpendicular to the loop, so the magnetic flux φ is given by:

    φ = BA

    B = magnetic field strength, A = loop area

    The area of the loop A is given by:

    A = πr²

    r = loop radius

    Make a substitution:

    φ = B2πr²

    Since the strength of the magnetic field is changing while the radius of the loop isn't changing, the change in magnetic flux Δφ is given by:

    Δφ = ΔB2πr²

    ΔB = change in magnetic field strength

    Make another substitution:

    ℰ = |ΔB2πr²/Δt|

    Given values:

    ΔB = 0.20T - 0.40T = - 0.20T, r = 0.50m, Δt = 2.5s

    Plug in and solve for ℰ:

    ℰ = | (-0.20) (2π) (0.50) ²/2.5|

    ℰ = 0.13V
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