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Question

A circular coil of radius 8 cm and 240 turns rotates at 45 rad/s in a 0.04 T field. What is the maximum
emf induced?

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Explanation

**Rotational emf** when coil area A rotates with angular speed ω in uniform field B, flux Φ = B A cos ωt, emf e = -N dΦ/dt = N B A ω sin ωt, maximum e₀ = N B A ω, frequency = ω/2π. For square side 22 cm area 0.0484 m² N=1 ω=14 rad/s B=0.15 T, e₀=1×0.15×0.0484×14=0.1016 V, sinusoidal. A = π r² = 3.14 × (0.08)² = 0.0201 m² . ε₀ = N B A ω = 240 × 0.04 × 0.0201 × 45 = 8.676 V ≈ 8.68 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N

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