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A circular coil of radius R having N turns rotates about its diameter in a uniform magnetic field B with constant angular speed omega. The resistance of the coil is eta ohms. The amplitude of the induced current in the coil is P * (N * B * omega * pi * R²) / (2 * eta). Find the value of P.

1. 1
2. 2
3. pi
4. 4

Correct answer: 2

Solution

For a coil rotating in a magnetic field: EMF = N * B * A * omega * sin(omega*t), where A = pi * R² is the area. The maximum (amplitude) of EMF is epsilon_max = N * B * pi * R² * omega. The amplitude of current = epsilon_max / eta = N * B * pi * R² * omega / eta. The given expression for amplitude is P * (N * B * omega * pi * R²) / (2*eta). Setting equal: N*B*pi*R²*omega / eta = P * N*B*omega*pi*R² / (2*eta). Therefore P/2 = 1 => P = 2.

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