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Magnetic Flux and Faraday's Laws of Induction

This category covers the fundamentals of magnetic flux and Faraday's laws of induction. It explains how magnetic fields interact with conductors to generate electromotive force, the mathematical relationships involved, and typical applications in physics and engineering.

30 questions

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

Ref: NCERT > Physics Book > Electromagnetic Induction > 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 =

Ref: NCERT > Physics Book > Electromagnetic Induction > 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

Ref: NCERT > Physics Book > Electromagnetic Induction > 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

Ref: NCERT > Physics Book > Electromagnetic Induction > 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.

Ref: NCERT > Physics Book > Electromagnetic Induction > 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

Ref: NCERT > Physics Book > Electromagnetic Induction > 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)

Ref: NCERT > Physics Book > Electromagnetic Induction > 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,

Ref: NCERT > Physics Book > Electromagnetic Induction > 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

Ref: NCERT > Physics Book > Electromagnetic Induction > 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

Ref: NCERT > Physics Book > Electromagnetic Induction > 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

Ref: NCERT > Physics Book > Electromagnetic Induction > 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 =

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