A closely wound rectangular coil of 80 turns has dimensions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it

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A closely wound rectangular coil of 80 turns has dimensions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 43.0 ∘ with a magnetic field of 1.40 T to a position perpendicular to the field. The rotation takes 0.0700 s . What is the average emf induced in the coil?

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  1. Answer:

    The average induced emf is 50.88 V

    Explanation:

    Given;

    number of turns, N = 80 turns

    angle between the plane of the coil and magnetic field, θ =  43°

    strength of magnetic field, B = 1.40 T

    time to make 80 turns = 0.0700 s

    [tex]Emf_{avg} = \frac{N \delta \phi}{dt} = N(\frac{BACos \theta {_f}-BACos \theta {_i}}{dt} )\\\\Emf_{avg} = \frac{NBA(Cos \theta {_f}-Cos \theta {_i})}{dt}[/tex]

    where;

    A is the area of the coil = 0.25 x 0.4 = 0.1 m²

    If the plane makes an angle of  43° with a magnetic field to a position perpendicular to the field, then the initial angle θi = 90 – 43 = 47° and the final angle θf  with the field = 0

    [tex]Emf_{avg} = \frac{NBA(Cos \theta {_f}-Cos \theta {_i})}{dt}\\\\Emf_{avg} = \frac{80*1.4*0.1(Cos(0)-Cos(47))}{0.07} = 50.88 \ V[/tex]

    Therefore, the average induced emf is 50.88 V

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