Magnetic Field & Induction

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

Was this helpful? Support seegongsik