#coil turns

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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Induced EMF Due to Change in Magnetic Field

A coil of 200 turns is placed in a field that decreases from 0.05 T to 0 in 0.4 s. If the area is 0.02 m², what is the i

**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 = 0.05 × 0.02 = 0.001 Wb . ε = N (Δ Φ/Δ t) = 200 × (0.001/0.4) = 0.5 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 =

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

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Induced EMF Due to Change in Magnetic Field

A coil of 90 turns and area 0.03 m² is in a field that increases from 0 to 0.06 T in 0.3 s. What is the induced emf?

**Uniform field change** in coil produces emf proportional to area and turns, for circular coil radius 0.16 m area πr²=0.0804 m², B 0.12 T deformed to wire in 0.6 s, ΔΦ=0.12×0.0804=0.00965 Wb, e=0.00965/0.6=0.0161 V, illustrating area change also induces emf. Δ Φ = B A = 0.06 × 0.03 = 0.0018 Wb . ε = N (Δ Φ/Δ t) = 90 × (0.0018/0.3) = 90 × 0.006 = 0.54 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 =

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

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Induced EMF Due to Change in Magnetic Field

A coil of 160 turns and area 0.06 m² is in a field that decreases from 0.08 T to 0 in 0.4 s. What is the induced emf?

**Uniform field change** in coil produces emf proportional to area and turns, for circular coil radius 0.16 m area πr²=0.0804 m², B 0.12 T deformed to wire in 0.6 s, ΔΦ=0.12×0.0804=0.00965 Wb, e=0.00965/0.6=0.0161 V, illustrating area change also induces emf. Δ Φ = B A = 0.08 × 0.06 = 0.0048 Wb . ε = N (Δ Φ/Δ t) = 160 × (0.0048/0.4) = 160 × 0.012 = 1.92 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 =

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

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Rotational EMF and AC Generator

A coil of 300 turns rotates at 100 rad/s in a 0.05 T field. If the area is 0.01 m², what is the maximum emf?

**Maximum emf** e₀ = N B A ω, for 180 turns A=0.02 m² B=0.03 T ω=60 rad/s, e₀=180×0.03×0.02×60=6.48 V, illustrating dependence on N, B, A, ω, used in generator design, increasing N or B or A or ω raises output. ε₀ = N B A ω = 300 × 0.05 × 0.01 × 100 = 15 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 15 V follows, reflecting Faraday's law and Lenz's opposition.

Ref: NCERT > Physics Book > Electromagnetic Induction > Rotational EMF and AC Generator

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Magnetic Flux and Faraday's Laws of Induction

In an AC generator, increasing the number of turns in the coil affects what aspect of the output?

**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. The emf ( ε = N B A ω sinω t ) is directly proportional to the number of turns, so more turns increase the amplitude of the induced emf. 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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