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Power dissipated by a coil rotating in a magnetic field (a.c. generator)

This type of question, asked 2 times: 16 May 2023 S2, 9 May 2024 S1. All 2 questions below, oldest first.

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  1. Question 1

    16 May 2023 S2

    1
    A circular coil of resistance RR, area AA, number of turns NN is rotated about its vertical diameter with angular speed ω\omega in a uniform magnetic field of magnitude BB. The average power dissipated in a complete cycle is

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  2. Question 2

    9 May 2024 S1

    9
    The coil of an a.c. generator has 100 turns, each of cross-sectional area 2 m² [the paper leaves the area blank; 2 m² is the value its answer key's working requires]. It is rotating at a constant angular speed of 30 rad/s in a uniform magnetic field of 2×10−22 \times 10^{-2} T. If the total resistance of the circuit is 600 Ω600\,\Omega, then the maximum power dissipated in the circuit is

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