#loop deformation

AC Generator, Back EMF and Time Duration of EMF

A circular loop of radius 10 cm is deformed into a straight wire in a 0.1 T field. If the flux change occurs in 0.2 s, w

**AC generator** emf e = N B A ω sin ωt, maximum when coil plane parallel to field, zero when perpendicular, time duration of emf when loop moves out of field t = L/v, L side along motion, v speed, e = B l v while cutting. For loop 0.28×0.14 m B=0.3 T v=1.4 m/s along longer side 0.28 m, cutting side 0.14 m, e=0.3×0.14×1.4=0.0588 V, duration t=0.28/1.4=0.2 s, emf exists only during exit. Initial flux: Φ = B A = 0.1 × π × (0.1)² = 0.00314 Wb . Final flux = 0. ε = (Δ Φ/Δ t) = (0.00314/0.2) = 0.0157 V ≈

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AC Generator, Back EMF and Time Duration of EMF

A circular loop of radius 14 cm is deformed into a straight wire in a 0.15 T field in 0.5 s. What is the induced emf?

**AC generator** emf e = N B A ω sin ωt, maximum when coil plane parallel to field, zero when perpendicular, time duration of emf when loop moves out of field t = L/v, L side along motion, v speed, e = B l v while cutting. For loop 0.28×0.14 m B=0.3 T v=1.4 m/s along longer side 0.28 m, cutting side 0.14 m, e=0.3×0.14×1.4=0.0588 V, duration t=0.28/1.4=0.2 s, emf exists only during exit. Initial flux: Φ = B A = 0.15 × π × (0.14)² = 0.00923 Wb . Final flux = 0. ε = (Δ Φ/Δ t) = (0.00923/0.5) = 0.01846 V ≈

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AC Generator, Back EMF and Time Duration of EMF

A circular loop of radius 11 cm is deformed into a straight wire in a 0.2 T field in 0.5 s. What is the induced emf?

**Back emf** in motor opposes applied voltage, e_b = N B A ω sin ωt, reduces net current, at start ω=0 e_b=0 current large, as speed increases e_b increases limiting current, power conversion mechanical, principle of motor and generator reciprocity. Initial flux: Φ = B A = 0.2 × π × (0.11)² = 0.0076 Wb . Final flux = 0. ε = (Δ Φ/Δ t) = (0.0076/0.5) = 0.0152 V ≈ 0.015 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt)

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AC Generator, Back EMF and Time Duration of EMF

A circular loop of radius 9 cm is deformed into a straight wire in a 0.25 T field in 0.4 s. What is the induced emf?

**Circular loop deformed into straight wire** in field B=0.12 T radius 16 cm area πr²=0.0804 m² flux 0.00965 Wb drops to zero in 0.6 s e=0.0161 V, illustrating flux change due to area change induces emf, even without B change, area deformation changes Φ = B A cosθ. Initial flux: Φ = B A = 0.25 × π × (0.09)² = 0.00636 Wb . Final flux = 0. ε = (Δ Φ/Δ t) = (0.00636/0.4) = 0.0159 V ≈ 0.016 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω

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AC Generator, Back EMF and Time Duration of EMF

A circular loop of radius 16 cm is deformed into a straight wire in a 0.12 T field in 0.6 s. What is the induced emf?

**Back emf** in motor opposes applied voltage, e_b = N B A ω sin ωt, reduces net current, at start ω=0 e_b=0 current large, as speed increases e_b increases limiting current, power conversion mechanical, principle of motor and generator reciprocity. Initial flux: Φ = B A = 0.12 × π × (0.16)² = 0.00965 Wb . Final flux = 0. ε = (Δ Φ/Δ t) = (0.00965/0.6) = 0.01608 V ≈ 0.016 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt)

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