Energy Stored in Inductor and Magnetic Energy

Energy Stored in Inductor and Magnetic Energy

A coil of 300 turns rotates at 70 rad/s in a 0.07 T field. If the area is 0.012 m², what is the maximum 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. ε₀ = N B A ω = 300 × 0.07 × 0.012 × 70 = 17.64 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 17.64 V follows, reflecting Faraday's law and Lenz's opposition.

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Energy Stored in Inductor and Magnetic Energy

A solenoid of 700 turns per meter and area 0.015 m² has a current drop from 8 A to 5 A in 0.3 s. What is the self-induce

**Magnetic energy density** u = B²/(2μ₀), for B=0.5 T, u=0.25/(2×4π×10⁻⁷)=0.25/(2.513×10⁻⁶)=99471 J/m³, large, but volume small, total energy moderate. Inductor stores energy in field, released when current interrupted causing spark. L = μ₀ n² A l , assume l = 1 m . L = 4π × 10⁻⁷ × (700)² × 0.015 × 1 = 0.00923 H . ε = L (Δ I/Δ t) = 0.00923 × (5 - 8/0.3) = 0.00923 × (-10) = 0.0923 V ≈ 0.092 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L

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Energy Stored in Inductor and Magnetic Energy

A coil of 120 turns and area 0.04 m² is in a 0.09 T field that drops to zero in 0.3 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 = 0.09 × 0.04 = 0.0036 Wb . ε = N (Δ Φ/Δ t) = 120 × (0.0036/0.3) = 120 × 0.012 = 1.44 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B

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Energy Stored in Inductor and Magnetic Energy

A solenoid of 1000 turns/m and area 0.01 m² has \( \mu_r = 2 \). What is its self-inductance? (\( \mu_0 = 4\pi \times 10

**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. L = μ_r μ₀ n² A l , assume l = 1 m . L = 2 × 4π × 10⁻⁷ × (1000)² × 0.01 × 1 = 0.02513 H ≈ 0.025 H . 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,

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Energy Stored in Inductor and Magnetic Energy

A solenoid of 700 turns/m and area 0.008 m² has \( \mu_r = 1 \). What is its self-inductance? (\( \mu_0 = 4\pi \times 10

**Magnetic energy density** u = B²/(2μ₀), for B=0.5 T, u=0.25/(2×4π×10⁻⁷)=0.25/(2.513×10⁻⁶)=99471 J/m³, large, but volume small, total energy moderate. Inductor stores energy in field, released when current interrupted causing spark. L = μ_r μ₀ n² A l , assume l = 1 m . L = 1 × 4π × 10⁻⁷ × (700)² × 0.008 × 1 = 0.00492 H ≈ 0.005 H . 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 0.005 H follows, reflecting Faraday's law and Lenz's opposition.

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Energy Stored in Inductor and Magnetic Energy

A solenoid of 550 turns per meter and area 0.016 m² has a current drop from 7 A to 4 A in 0.3 s. What is the self-induce

**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. L = μ₀ n² A l , assume l = 1 m . L = 4π × 10⁻⁷ × (550)² × 0.016 × 1 = 0.00608 H . ε = L (Δ I/Δ t) = 0.00608 × (4 - 7/0.3) = 0.00608 × (-10) = 0.0608 V ≈ 0.061 V . Using

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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

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Energy Stored in Inductor and Magnetic Energy

A conducting loop is placed in a magnetic field that remains constant in magnitude and direction. No emf is induced beca

**Magnetic energy density** u = B²/(2μ₀), for B=0.5 T, u=0.25/(2×4π×10⁻⁷)=0.25/(2.513×10⁻⁶)=99471 J/m³, large, but volume small, total energy moderate. Inductor stores energy in field, released when current interrupted causing spark. Emf is induced only when magnetic flux changes. A constant field with a stationary loop results in no flux change, hence 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 N²A/l, M = e/(dI/dt) and U = ½ L I², result No change in magnetic flux follows, reflecting Faraday's law and Lenz's opposition.

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Energy Stored in Inductor and Magnetic Energy

A coil of 80 turns is placed in a magnetic field that increases from 0 to 0.03 Wb/m² in 0.2 s. If the coil area is 0.05

**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. Flux change: Δ Φ = B A = 0.03 × 0.05 = 0.0015 Wb . ε = N (Δ Φ/Δ t) = 80 × (0.0015/0.2) = 80 × 0.0075 = 0.6 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

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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

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Energy Stored in Inductor and Magnetic Energy

A coil of 130 turns and area 0.03 m² is rotated at 30 Hz in a 0.08 T field. What is the maximum 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. ω = 2π v = 2π × 30 = 60π rad/s . ε₀ = N B A ω = 130 × 0.08 × 0.03 × 60π = 58.62 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 58.62 V follows,

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Energy Stored in Inductor and Magnetic Energy

A coil of self-inductance 1.0 H has its current decreased from 5 A to 2 A in 0.15 s. What is the magnitude of the induce

**Magnetic energy density** u = B²/(2μ₀), for B=0.5 T, u=0.25/(2×4π×10⁻⁷)=0.25/(2.513×10⁻⁶)=99471 J/m³, large, but volume small, total energy moderate. Inductor stores energy in field, released when current interrupted causing spark. ε = L (Δ I/Δ t) . Δ I = 2 - 5 = -3 A , Δ t = 0.15 s . ε = 1.0 × (-3/0.15) = 1.0 × (-20) = -20 V , magnitude = 20 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

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