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A single coil of wire, with a radius of 0.13 m is rotated in a uniform magnetic field such that the angle between the field vector and the area vector obeys θ=ωt. If the strength of the field is 3.746 T, and the angular frequency is 524.7 rad/s, what is the induced emf in the loop at t=1.16 s?

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onyebuchinnaji

The magnitude of emf induced in the single coil of wire rotated in the uniform magnetic field is 0.171 V.


Induced emf

The emf induced in the loop is determined by applying Faraday's law of electromagnetic induction.

emf = N(dФ/dt)

where;

  • N is number of turns of the wire
  • Ф is magnetic flux

Ф = BA

where;

  • B is magnetic field strength
  • A is the area of the loop

emf = NBA/t

A = πr²

A = π x (0.13)²

A = 0.053 m²

emf = NBA/t

emf = (1 x 3.746 x 0.053)/(1.16)

emf = 0.171 V

Thus, the magnitude of emf induced in the single coil of wire is 0.171 V.

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