#magnetic field change

Lenz's Law, Eddy Currents and Applications

A conducting loop is placed in a uniform magnetic field with its plane parallel to the field lines. Why is no emf induce

**Solenoid second coil** experiences emf only when current in solenoid changes because flux linkage changes only then, steady current gives constant Φ, dΦ/dt=0, no emf, when current changes, dΦ/dt ≠0, emf induced, illustrating Faraday's law requirement of changing flux. When the plane is parallel to the field, the flux through the loop is zero ( Φ = B A cos 90° = 0 ), so changing the field strength does not alter the flux, resulting in no emf. Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀

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 coil of 130 turns and area 0.04 m² is in a field that increases from 0 to 0.05 T in 0.2 s. What is the induced emf?

**Energy in inductor** cannot change instantaneously because that would require infinite power, current through inductor continuous, voltage may jump, principle used in chokes, inductive kick, back emf, explaining why inductor opposes change in current. Δ Φ = B A = 0.05 × 0.04 = 0.002 Wb . ε = N (Δ Φ/Δ t) = 130 × (0.002/0.2) = 130 × 0.01 = 1.3 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 1.3 V

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 130 turns and area 0.08 m² is in a 0.12 T field that drops to zero in 0.4 s. What is the induced 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. Δ Φ = B A = 0.12 × 0.08 = 0.0096 Wb . ε = N (Δ Φ/Δ t) = 130 × (0.0096/0.4) = 130 × 0.024 = 3.12 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,

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 0.05 m² is in a field that increases from 0 to 0.06 T 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 = 0.06 × 0.05 = 0.003 Wb . ε = N (Δ Φ/Δ t) = 150 × (0.003/0.3) = 150 × 0.01 = 1.5 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 =

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 solenoid of 400 turns per meter and area 0.015 m² has a current drop from 5 A to 2 A in 0.3 s. What is the self-induce

**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. L = μ₀ n² A l , assume l = 1 m . L = 4π × 10⁻⁷ × (400)² × 0.015 × 1 = 0.003016 H . ε = L (Δ I/Δ t) = 0.003016 × (2 - 5/0.3) = 0.003016 × (-10) = 0.03016 V ≈ 0.03 V . Using Φ = B A cosθ, e = -N dΦ/dt

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

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Magnetic Flux and Faraday's Laws of Induction

A circular loop is placed in a uniform magnetic field, and the field strength is increased steadily. What determines the

**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. According to Faraday’s law, the induced emf depends on the rate of change of magnetic flux, which increases with the rate at which the magnetic field strength changes. Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v =

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

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