Magnetic Field & Induction

When the magnetic flux through a coil changes, a current is induced. If the flux is steady, nothing happens. Moving a magnet faster raises the rate of flux change and the induced emf. That is electromagnetic induction, the idea behind generators and transformers. Slide the flux change rate here to see how the induced emf grows.

Changing Flux Drives a Current

Flux change rate ΔΦ/Δt2

👀 See It

①If the flux through the coil is constant, nothing happens

②Moving a magnet — changing the flux — induces a current in the coil

③The faster the flux changes (steeper slope), the larger the induced emf

Field, Flux, Induced EMF

Magnetic flux

Φ = B A

The product of field B and area A — the field lines passing perpendicular through the coil

Faraday's law

V = N ΔΦΔt

Induced emf magnitude proportional to turns N and flux rate ΔΦ/Δt

Lenz's Law — Direction

🧲 Opposing the Change

①The induced current flows so as to oppose the change in flux (Lenz's law)

②If flux grows it acts to reduce it; if it shrinks, to increase it

③A consequence of energy conservation — no free current

Compute It Directly

Example 1

The flux through a single-turn coil changes from 0.1 Wb to 0.5 Wb in 0.2 s. Find the induced emf magnitude.

Flux change ΔΦ = 0.5 − 0.1 = 0.4 Wb.

Put N=1, Δt=0.2 into V = N·ΔΦ/Δt.

V = 1 × 0.40.2 = 2 V

▸ 2 V

Divide the change (Wb) by the time (s) — not the flux itself.

Example 2

The flux through a 100-turn coil changes by 0.02 Wb in 0.01 s. Find the induced emf magnitude.

Multiply by the number of turns N=100.

V = N ΔΦΔt

V = 100 × 0.02/0.01.

V = 100 × 2 = 200 V

▸ 200 V

Forgetting the turns N makes the answer N times too small.

Wrap-up

Key result

Φ = B A, V = N ΔΦΔt

Flux is B×A; induced emf is turns × flux rate

2021 CSAT Science (Physics Ⅰ) type, adapted

The flux through a 200-turn coil changes uniformly by 0.3 Wb in 0.1 s. What is the induced emf magnitude?

①60 V

②200 V

③300 V

④600 V

⑤900 V

▸ ④ 600 V

Put N=200, ΔΦ=0.3, Δt=0.1 into V = N·ΔΦ/Δt.

V = 200 × 0.30.1

Compute.

V = 200 × 3 = 600 V

🎯 Exam Points

①flux Φ = BA

②Faraday V = N·ΔΦ/Δt (turns N essential)

③Lenz's law: opposes the change

④constant flux means zero induced current

⑤V is proportional to the rate — faster means larger

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Current & Resistance

Physics II · Uniform Circular Motion

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