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A single-turn rectangular coil of area A rotates in a uniform magnetic field B with angular velocity omega about an axis perpendicular to the field. Initially the plane of the coil is perpendicular to the field. The average induced EMF as the coil rotates through 90 degrees is:

1. 2*omega*B*A/pi
2. omega*B*A/pi
3. omega*B*A/(2*pi)
4. omega*B*A/(4*pi)

Correct answer: 2*omega*B*A/pi

Solution

Initially the plane is perpendicular to B, so the area vector is parallel to B and flux = BA (maximum). After rotating 90 deg the plane is parallel to B, so flux = 0. Change in flux = BA - 0 = BA (magnitude). Time = (pi/2)/omega. Average EMF = delta_flux / deltaₜ = BA / ((pi/2)/omega) = 2*omega*B*A/pi.

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