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A square-shaped coil of edge a having  n turns is rotated with a uniform angular velocity ω  about one of its diagonals which is kept fixed in a horizontal position. A uniform magnetic field   exists in the vertical direction. Find the emf induced in the  coil.
 

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a
6nBa2ωsinωt
b
3nBa2ωsinωt
c
nBa2ωsinωt
d
2nBa2ωsinωt

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detailed solution

Correct option is C

The area of the square frame is A=a2 . If the normal to the frame makes an angle  with the magnetic field at t =0, this angle will become θ=ωt after some time . 

The flux of the  magnetic field at this time is .Φ=nBAcosθ=nBa2cosωt
The induced emf is ε=dt=nBa2ωsinωt
Thus, an alternating emf is induced in the coil.
 

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