#spoked wheel

Lenz's Law, Eddy Currents and Applications

A wheel with 8 spokes of 0.55 m each rotates at 50 rpm in a 0.4 T field. What is the induced emf?

**Eddy currents** are circulating currents induced in bulk conductor by changing flux, oppose motion, cause damping, heating, energy loss, minimized by laminating core into thin sheets insulated, increasing resistance, reducing eddy current magnitude, used in induction heating and braking. ω = 2π × (50/60) = (5π/3) rad/s . ε = (1/2) B ω R² = (1/2) × 0.4 × (5π/3) × (0.55)² = 0.3166 V ≈ 0.317 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) and U = ½ L

Ref: NCERT > Physics Book > Electromagnetic Induction > Lenz's Law, Eddy Currents and Applications

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Energy Stored in Inductor and Magnetic Energy

A wheel with 5 spokes of 0.4 m each rotates at 30 rpm in a 0.7 T field. What is the induced emf?

**Energy stored in inductor** U =½ L I² (J), L inductance (H), I current (A), resides in magnetic field, energy density u = B²/(2μ₀) (J/m³), B field (T), μ₀=4π×10⁻⁷ H/m. For solenoid B=μ₀ n I, volume V= A l, U = (B²/2μ₀) V =½ (μ₀ n² A l) I² =½ L I², consistent. ω = 2π × (30/60) = π rad/s . ε = (1/2) B ω R² = (1/2) × 0.7 × π × (0.4)² = 0.1759 V ≈ 0.176 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A

Ref: NCERT > Physics Book > Electromagnetic Induction > Energy Stored in Inductor and Magnetic Energy

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Self-Induction and Self-Inductance

A wheel with 6 spokes of 0.6 m each rotates at 45 rpm in a 0.5 T field. What is the induced emf?

**Self-inductance of solenoid** L = μ₀ N² A / l, N total turns, A cross-section, l length, for N=650 turns per meter means n=650 m⁻¹, if length 1 m N=650, A=0.014, L=4π×10⁻⁷×650²×0.014/1=0.00743 H, self-induced emf magnitude L |dI/dt|, dI/dt=12 A/s, e=0.089 V, opposes change. ω = 2π × (45/60) = 1.5π rad/s . ε = (1/2) B ω R² = (1/2) × 0.5 × 1.5π × (0.6)² = 0.8478 V ≈ 0.85 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)

Ref: NCERT > Physics Book > Electromagnetic Induction > Self-Induction and Self-Inductance

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Magnetic Flux and Faraday's Laws of Induction

A wheel with 8 spokes of 0.25 m each rotates at 60 rpm in a 0.5 T field. What is the induced emf?

**Magnetic flux** Φ = B·A = B A cosθ, B magnetic field (T), A area (m²), θ angle between B and normal to area, unit Wb = T·m², Faraday's law induced emf e = -N dΦ/dt, N turns, negative sign Lenz's law indicating opposition, magnitude |e| = N |ΔΦ/Δt|, for 100 turns ΔΦ=0.03 Wb Δt=0.06 s e=100×0.03/0.06=50 V. ω = 2π × (60/60) = 2π rad/s . ε = (1/2) B ω R² = (1/2) × 0.5 × 2π × (0.25)² = 0.098 V ≈ 0.1 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l

Ref: NCERT > Physics Book > Electromagnetic Induction > Magnetic Flux and Faraday's Laws of Induction

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