FARADAY
DAY 2026

ELECTROMAGNETIC INDUCTION

ε = −N · dΦ/dt
FARADAY DAY
INDUCTION GENERATOR TRANSFORMER EM WAVE LAWS TIMELINE

A changing magnetic field creates electricity.

Faraday's 1831 discovery of induction is the principle behind every generator, transformer and motor in the power grid.

LAB 01

Faraday's Law — magnet & coil

The induced EMF depends on how fast the flux changes, not on the flux itself. Tap DRAG MAGNET and slide it with your finger — stop moving and the EMF collapses to zero.

Φ    = 0.000 Wb
dΦ/dt = 0.000 Wb/s
ε    = 0.000 V
Green needle shows induced current direction — Lenz's law always opposes the change.
LAB 02

AC Generator — rotating loop

A loop rotating in a uniform field sweeps flux sinusoidally. EMF is the derivative, so it peaks when the loop lies parallel to the field — exactly where flux is zero.

θ  = 0°
Φ  = 0.000 Wb
ε  = 0.000 V
ε̂  = 0.000 V
Cyan = flux Φ · orange = EMF ε. Note the 90° phase shift.
LAB 03

Transformer — mutual induction

Two coils share one iron core. The same changing flux links both windings, so voltage scales with the turns ratio while current scales inversely.

N₁/N₂ = 4.00
U₂ = 100 V
I₂ = 40.0 A
S  = 4.0 kVA
LAB 04

Electromagnetic wave

Faraday's induction plus Maxwell's displacement current: a changing E-field makes a B-field and vice versa — a self-sustaining wave travelling at c, E ⟂ B ⟂ propagation.

E-field cyan — vertical
B-field violet — horizontal
c = 2.998 × 10⁸ m/s
REFERENCE

The laws behind the animation

Faraday's law of induction

ε = −N · dΦ/dt

The EMF induced in a circuit equals the negative rate of change of flux linkage. Only change induces voltage.

Magnetic flux

Φ = ∫ B · dA = B·A·cos θ

Flux counts the field lines crossing a surface. Changing B, the area or the orientation changes Φ.

Lenz's law

direction: oppose the change

The induced current flows so its own field opposes the change that created it — the minus sign, and energy conservation.

Maxwell–Faraday equation

∇ × E = −∂B/∂t

The field form of Faraday's law: a time-varying magnetic field produces a circulating electric field, no wire required.

Ampère–Maxwell law

∇ × B = μ₀(J + ε₀ ∂E/∂t)

Currents and changing electric fields both create magnetic fields. With Faraday's law this yields the EM wave.

Transformer relation

U₁/U₂ = N₁/N₂ = I₂/I₁

Mutual induction through a shared core. Ideal lossless transfer: U₁I₁ = U₂I₂.

TIMELINE

From a ring of iron to the grid

1820 — ØrstedA current deflects a compass needle: electricity and magnetism are linked.
1831 — Induction ringA changing current in one winding induces a momentary current in a second winding on the same iron ring.
1831 — Disc dynamoA copper disc rotating between magnet poles delivers continuous current: the first generator.
1834 — LenzThe direction of the induced current is fixed by opposition to the change.
1865 — MaxwellFaraday's field picture cast in equations, predicting waves at the speed of light.
TodayEvery generator, transformer, motor and switchgear bay in the grid runs on ε = −N dΦ/dt.