A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a un

Question

A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s . What emf is induced in the loop at that instant

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Huyền Thanh 4 years 2021-07-14T04:52:08+00:00 1 Answers 53 views 0

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  1. lethu
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    2021-07-14T04:53:53+00:00
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    Answer:

    The induced emf in the loop is 0.452 volts.

    Explanation:

    Given that,

    Radius of the circular loop, r = 12 cm = 0.012 m

    Magnetic  field, B = 0.8 T    

    When released, the radius of the loop starts to shrink at an instantaneous rate of, \dfrac{dr}{dt}=75\ cm/s=0.75\ m/s

    The induced emf in the loop is equal to the rate of change of magnetic flux. It is given by :

    \epsilon=\dfrac{-d\phi}{dt}\\\\\epsilon=\dfrac{-d(BA)}{dt}\\\\\epsilon=B\dfrac{-d(\pi r^2)}{dt}\\\\\epsilon=2\pi rB\dfrac{-dr}{dt}\\\\\epsilon=2\pi \times 0.12\times 0.8\times 0.75\\\\\epsilon=0.452\ V

    So, the induced emf in the loop is 0.452 volts.

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