Mr. Scandrett's ClassroomOS

Physics · Lesson 10

Faraday's Law

Electromagnetic Induction Changing Flux → Voltage Generators & Transformers

Michael Faraday discovered in 1831 that a changing magnetic field through a wire loop produces a voltage. This single idea is the foundation of every electric generator, transformer, and induction motor ever built.

Michael Faraday (1791–1867)

Michael Faraday was a self-taught English scientist who started as a bookbinder's apprentice and became one of history's greatest experimenters. With little formal mathematics, he discovered electromagnetic induction, the laws of electrolysis, and the relationship between light and magnetism. James Clerk Maxwell later put Faraday's ideas into the mathematical equations that unified electricity, magnetism, and light.

The Law

The induced electromotive force (EMF) in a loop is equal to the negative rate of change of magnetic flux through that loop:

Key insight: It is the change in flux that matters — not the flux itself. A strong, constant magnetic field through a loop induces nothing. Only when the field changes (or the loop moves) does voltage appear.

What is Magnetic Flux?

Magnetic flux (Φ) is a measure of how many field lines pass through a surface: Φ = B × A × cos θ, where B is the field strength, A is the area of the loop, and θ is the angle between the field and the surface normal. Flux changes when B changes, when the loop area changes, or when the loop rotates relative to the field.

Interactive Simulator

The loop rotates in the magnetic field. Watch flux and induced EMF change over time. Adjust field strength and rotation speed in the panel.

Flux Φ0.00 Wb
EMF0.00 V
Angle θ0°

Real-World Applications

⚡
AC GeneratorsRotating coils in magnetic fields continuously change flux, producing the alternating current that powers the electrical grid.
🔌
TransformersAlternating current in one coil creates a changing flux in an iron core, which induces voltage in a second coil — stepping voltage up or down.
🚗
Electric MotorsThe reverse of generation: a changing current creates a changing flux, which induces forces that spin the motor shaft.
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Induction CooktopsRapidly changing current creates rapidly changing flux under the cooking surface, inducing eddy currents that heat the pan directly.

Practice Problems

Use EMF = N × ΔΦ/Δt.

Easy1. A single loop (N=1) has flux change of 0.5 Wb in 0.5 s. What is the induced EMF?

Hint: EMF = 1 × 0.5/0.5 = 1 V

Easy2. The flux through a coil is constant at 2 Wb. What is the induced EMF?

Hint: No change in flux → no induced EMF → 0 V

Medium3. A 200-turn coil has its flux reduced from 0.3 Wb to 0.1 Wb in 0.02 s. What is the magnitude of the induced EMF?

Hint: EMF = 200 × (0.2)/0.02 = 2000 V

Challenge4. A generator coil (N=100, area=0.05 m²) rotates at 50 Hz in a 0.8 T field. Peak EMF = NBAω where ω=2πf. Calculate the peak EMF (round to nearest V).

Hint: ω = 2π×50 ≈ 314 rad/s; EMF = 100×0.8×0.05×314 ≈ 1257 V

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