An elastic conducting material is stretched into a circular loop of 10.7 cm radius. It is placed with its plane perpendicular to a uniform 0

Question

An elastic conducting material is stretched into a circular loop of 10.7 cm radius. It is placed with its plane perpendicular to a uniform 0.803 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 81.0 cm/s. What emf is induced in volts in the loop at that instant?

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RuslanHeatt 5 years 2021-07-31T12:38:24+00:00 1 Answers 25 views 0

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  1. Verity
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    2021-07-31T12:39:34+00:00
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    Answer:

    0.44 V

    Explanation:

    Parameters given:

    Radius of loop, r = 10.7 cm = 0.107 m

    Magnetic field strength, B = 0.803 T

    Rate of shrinkage of Radius, dr/dt = 81 cm/s = 0.81m/s

    EMF induced is given in terms of magnetic Flux, Φ, as:

    EMF = dΦ/dt

    Magnetic Flux, Φ, is given as:

    Φ = B * A (where A is area of loop)

    Therefore, EMF is:

    EMF = d(B*A)/dt

    The area of the loop is given as A = πr²

    EMF = d(Bπr²) / dt = Bπ*d(r²)/dt

    => EMF = Bπ*2r*(dr/dt)

    EMF = 0.803 * π * 2 * 0.107 * 0.81

    EMF = 0.44 V

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