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#coil area

4 public questions tagged with this topic.

Energy Stored in Inductor and Magnetic Energy

A coil of 170 turns and area 0.07 m² is in a field that decreases from 0.1 T to 0 in 0.5 s. 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. Δ Φ = B A = 0.1 × 0.07 = 0.007 Wb . ε = N (Δ Φ/Δ t) = 170 × (0.007/0.5) = 170 × 0.014 = 2.38 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B

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

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Mutual Induction and Mutual Inductance

A coil of 230 turns rotates at 85 rad/s in a 0.03 T field. If the area is 0.02 m², what is the maximum emf?

**Solenoid carries steady current** second coil experiences emf only when current in solenoid changes because dΦ/dt ≠0 only when I changes, steady current gives constant flux, no induction, illustrating Faraday's law requires changing flux, not static field. ε₀ = N B A ω = 230 × 0.03 × 0.02 × 85 = 11.73 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 I², result 11.73 V follows, reflecting Faraday's law and Lenz's opposition.

Ref: NCERT > Physics Book > Electromagnetic Induction > Mutual Induction and Mutual Inductance

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Induced EMF Due to Change in Magnetic Field

A coil of 150 turns and area 0.06 m² is in a 0.14 T field that drops to zero in 0.3 s. What is the induced emf?

**Field decreasing to zero** induces emf trying to maintain field, current direction such that its field adds to original. For 150 turns area 0.06 m² B 0.14 T to zero in 0.3 s, e=150×0.06×0.14/0.3=4.2 V, as earlier, showing linear dependence on N, A, ΔB/Δt. Δ Φ = B A = 0.14 × 0.06 = 0.0084 Wb . ε = N (Δ Φ/Δ t) = 150 × (0.0084/0.3) = 150 × 0.028 = 4.2 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 =

Ref: NCERT > Physics Book > Electromagnetic Induction > Induced EMF Due to Change in Magnetic Field

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