Electromagnetic Induction

Move a magnet near a coil and current flows; stop the magnet and the current vanishes. What matters is the change in magnetic flux, and a larger rate of change means a larger induced emf. Faraday's law writes that link as an equation. Slide the flux change rate dΦ/dt here to see how the induced emf responds.

Move a Magnet, Get Current!

🧲 Faraday's Discovery

①Move a magnet near a coil and current flows!

②Stop the magnet and the current disappears

③Key: it is the change in magnetic flux that creates current

Visualizing Electromagnetic Induction

Flux change rate dΦ/dt5 Wb/s

💡 Key Observations

①Larger dΦ/dt → larger induced EMF

②Increasing flux → induced current opposes the increase (Lenz)

③No flux change → no induced EMF

Faraday's Law

Faraday's Law of Induction

ε = -dΦdt

EMF = negative of time rate of change of magnetic flux

Coil with N Turns

ε = -NdΦdt

More turns N → larger induced EMF

Magnetic Flux

Φ = BA cosθ

Φ: flux (Wb), B: field (T), A: area (m²), θ: angle between B and area normal

Lenz's Law

🔄 Lenz's Law: nature dislikes change

①Induced current direction opposes the change in flux!

②Flux increases → induced current makes opposite-direction field

③Flux decreases → induced current makes same-direction field

④This is the meaning of the minus sign in the formula!

Worked Examples

Example 1

The magnetic flux through a 200-turn coil changes by 0.01 Wb over 0.5 s. What is the magnitude of the induced EMF?

Apply Faraday’s law ε = N(ΔΦ/Δt) in magnitude.

ε = NΔΦΔt

Substitute N = 200, ΔΦ = 0.01 Wb, Δt = 0.5 s.

ε = 200 × 0.010.5 = 4 V

▸ 4 V

Induced EMF is turns × rate of flux change. The minus sign is direction (Lenz); use magnitudes for the size.

Example 2

A magnetic field perpendicular to a single 0.5 m² loop rises from 0.1 T to 0.3 T in 0.2 s. What is the induced EMF?

With Φ = BA (θ=0), the flux change is ΔΦ = ΔB·A.

ΔΦ = ΔB·A = (0.3 - 0.1) × 0.5 = 0.1 Wb

Substitute into ε = ΔΦ/Δt.

ε = 0.10.2 = 0.5 V

▸ 0.5 V

From Φ = BA cosθ, if only B changes then ΔΦ = A·ΔB. With fixed area and angle, a changing field alone induces an EMF.

Summary

Faraday's Law (Core)

ε = -NdΦdt

EMF = -turns × flux change rate

CSAT-style

A coil has induced EMF ε. If the number of turns is doubled and the rate of flux change is also doubled, what is the induced EMF?

①2ε

②3ε

③4ε

④ε2

⑤6ε

▸ ③ 4ε

Since ε = N(dΦ/dt), it is proportional to both N and dΦ/dt.

ε = NdΦdt

2× turns × 2× rate = 4×.

(2N)(2dΦdt) = 4NdΦdt = 4ε

🎯 Exam Points

①ε = -NdΦ/dt: larger flux change or more turns → bigger EMF

②Lenz: induced current opposes flux change

③Φ = BAcosθ: changing area, field, or angle induces EMF

④Generator: coil rotation → θ changes → Φ changes → EMF

⑤Transformer: ε₁/ε₂ = N₁/N₂ (turns ratio for voltage)

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Electric Field and Gauss's Law

Interference and Diffraction

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