Magnetic Flux and Faraday's Laws of Induction

Magnetic Flux and Faraday's Laws of Induction

A magnet is moved away from a coil, and the induced current flows clockwise as viewed from the magnet. What is the polar

**Faraday's first law** emf induced when flux linking coil changes, second law magnitude proportional to rate of change, e = -dΦ/dt, for N turns e = -N dΦ/dt, flux Φ = B A cosθ, change can be due to B change, A change, or θ change, all produce emf. By Lenz’s law, the clockwise current opposes the decreasing flux by producing a south pole facing the receding north pole of the magnet, creating an attractive force. 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

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Magnetic Flux and Faraday's Laws of Induction

A conducting loop is shrunk in a uniform magnetic field. The induced current flows in a direction to oppose what change?

**Faraday's first law** emf induced when flux linking coil changes, second law magnitude proportional to rate of change, e = -dΦ/dt, for N turns e = -N dΦ/dt, flux Φ = B A cosθ, change can be due to B change, A change, or θ change, all produce emf. Shrinking the loop decreases the magnetic flux through it. Lenz’s law states the induced current opposes this decrease by creating a field in the same direction as the original field. 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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Magnetic Flux and Faraday's Laws of Induction

A wheel with 10 spokes of 0.7 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 × (0.7)² = 0.7697 V ≈ 0.77 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l

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Magnetic Flux and Faraday's Laws of Induction

A coil of self-inductance 0.4 H has its current decreased from 5 A to 2 A in 0.1 s. What is the magnitude of the induced

**Flux change example** coil 150 turns area 0.06 m² B 0.14 T drops to zero in 0.3 s, ΔΦ = B A =0.14×0.06=0.0084 Wb per turn, ΔΦ/Δt=0.028 Wb/s, e=150×0.028=4.2 V, illustrating calculation from B and area. ε = -L (Δ I/Δ t) . Δ I = 2 - 5 = -3 A , Δ t = 0.1 s . ε = 0.4 × (-3/0.1) = 0.4 × (-30) = -12 V . Magnitude = 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

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Magnetic Flux and Faraday's Laws of Induction

A magnet is oscillated near a coil. The induced emf in the coil alternates because of what characteristic of the magnet’

**Flux change example** coil 150 turns area 0.06 m² B 0.14 T drops to zero in 0.3 s, ΔΦ = B A =0.14×0.06=0.0084 Wb per turn, ΔΦ/Δt=0.028 Wb/s, e=150×0.028=4.2 V, illustrating calculation from B and area. The oscillatory motion causes the magnetic flux to alternately increase and decrease, inducing an alternating emf as the flux change direction reverses. 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 Periodic change in flux direction follows, reflecting Faraday's law and Lenz's opposition.

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Magnetic Flux and Faraday's Laws of Induction

A coil of 120 turns experiences a magnetic flux change from 0 to 0.04 Wb in 0.08 s. What is the induced emf?

**Faraday's first law** emf induced when flux linking coil changes, second law magnitude proportional to rate of change, e = -dΦ/dt, for N turns e = -N dΦ/dt, flux Φ = B A cosθ, change can be due to B change, A change, or θ change, all produce emf. ε = N (Δ Φ/Δ t) . Δ Φ = 0.04 Wb , Δ t = 0.08 s , N = 120 . ε = 120 × (0.04/0.08) = 120 × 0.5 = 60 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N

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Magnetic Flux and Faraday's Laws of Induction

A metal plate swings like a pendulum through a magnetic field. The slowing of its motion is primarily due to what?

**Faraday's first law** emf induced when flux linking coil changes, second law magnitude proportional to rate of change, e = -dΦ/dt, for N turns e = -N dΦ/dt, flux Φ = B A cosθ, change can be due to B change, A change, or θ change, all produce emf. The motion induces currents in the plate, which produce an opposing magnetic field, exerting a force that resists the motion (Lenz’s law), slowing it down. 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)

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Magnetic Flux and Faraday's Laws of Induction

A bar magnet is pushed towards a coil with its north pole first, then pulled back. The direction of the induced current

**Flux change example** coil 150 turns area 0.06 m² B 0.14 T drops to zero in 0.3 s, ΔΦ = B A =0.14×0.06=0.0084 Wb per turn, ΔΦ/Δt=0.028 Wb/s, e=150×0.028=4.2 V, illustrating calculation from B and area. Lenz’s law causes the current to oppose the flux change: it creates a north pole to repel the approaching magnet and a south pole to attract it during withdrawal, reversing the direction. 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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Magnetic Flux and Faraday's Laws of Induction

A coil is placed in a time-varying magnetic field. The direction of the induced current is determined by which principle

**Faraday's first law** emf induced when flux linking coil changes, second law magnitude proportional to rate of change, e = -dΦ/dt, for N turns e = -N dΦ/dt, flux Φ = B A cosθ, change can be due to B change, A change, or θ change, all produce emf. Lenz’s law dictates that the induced current opposes the change in magnetic flux, determining its direction based on the field’s variation. 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

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Magnetic Flux and Faraday's Laws of Induction

A conducting rod is rotated about one end in a uniform magnetic field. The emf induced between the ends is due to what f

**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 rotation causes charges to move through the field, experiencing a magnetic force (Lorentz force) that separates them, inducing an emf along the rod. Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω

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Magnetic Flux and Faraday's Laws of Induction

A coil of 100 turns and area 0.03 m² is in a 0.08 T field that drops to zero in 0.2 s. What is the induced emf?

**Flux change example** coil 150 turns area 0.06 m² B 0.14 T drops to zero in 0.3 s, ΔΦ = B A =0.14×0.06=0.0084 Wb per turn, ΔΦ/Δt=0.028 Wb/s, e=150×0.028=4.2 V, illustrating calculation from B and area. Δ Φ = B A = 0.08 × 0.03 = 0.0024 Wb . ε = N (Δ Φ/Δ t) = 100 × (0.0024/0.2) = 100 × 0.012 = 1.2 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 = e/(dI/dt) and U = ½ L I², result

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Magnetic Flux and Faraday's Laws of Induction

A wheel with 5 spokes of 0.65 m each rotates at 42 rpm in a 0.7 T field. What is the induced emf?

**Faraday's first law** emf induced when flux linking coil changes, second law magnitude proportional to rate of change, e = -dΦ/dt, for N turns e = -N dΦ/dt, flux Φ = B A cosθ, change can be due to B change, A change, or θ change, all produce emf. ω = 2π × (42/60) = 1.4π rad/s . ε = (1/2) B ω R² = (1/2) × 0.7 × 1.4π × (0.65)² = 0.623 V ≈ 0.62 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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