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A coil having 1000 turns and area 0.10 m² rotates at half a revolution per second in a uniform magnetic field of 0.01 T perpendicular to the axis of rotation of the coil. The maximum emf generated in the coil is _____ V.

Asked in GUJCET 2020 · Peak and instantaneous EMF

• (1) 3.14
• (2) 5.0
• (3) 0.5
• (4) 0.314

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 5.0 V. Sanity check: NAB = 1000×0.10×0.01 = 1 Wb, so the peak emf in volts equals ω; 5.0 V would need ω = 5 rad s⁻¹, not π.
• (3) Uses the frequency 0.5 rev s⁻¹ in place of the angular speed, forgetting the 2π: 1000×0.10×0.01×0.5 = 0.5 V.
• (4) No single slip gives 0.314 V; it is a tenth of the right value and would need an area of only 0.01 m². With the given data NABω = 1×π ≈ 3.14 V.

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