LearnYPH11WPH14 · Unit 4: Further Mechanics, Fields and ParticlesElectric and magnetic fieldsElectromagnetic induction

Electric and magnetic fields · Subtopic 10 of 10

Electromagnetic Induction

Magnetic flux through an area is $\Phi=BA$ (with $B$ perpendicular to $A$ ), measured in webers. For a coil of $N$ turns, flux linkage is $N\Phi$ . Faraday's law: the induced e.m.f. equals the rate of change of flux linkage. Lenz's law: the induced e.m.f. acts to oppose the change that causes it. Together: $E=-\dfrac{\Delta(N\Phi)}{\Delta t}$ . A conductor of length $L$ moving at $v$ through a field $B$ has $E=BLv$ .

Cambridge 9702 Paper 4Edexcel YPH11 WPH14AQA 7408 Paper 2≈ 40 minRevision 6 · updated 2026-10-27

Section 1 of 14

Learning objectives

Define magnetic flux and flux linkage; use $\Phi=BA$ .
State Faraday's and Lenz's laws.
Use $E=-\dfrac{\Delta(N\Phi)}{\Delta t}$ and $E=BLv$ .
Explain the direction of induced currents in terms of energy conservation.

Pause and think

A magnet dropped through a copper tube falls very slowly, though copper isn't magnetic. Why?

Section 2 of 14

Core idea

Start hereA magnet that falls slowly

Drop a strong magnet down a copper pipe and it drifts down as if through honey, though copper isn't magnetic. The falling magnet induces currents in the pipe, and those currents push back. Changing magnetic flux always fights its own change.

The big idea

$\Phi=BA$ ; linkage $N\Phi$ . Faraday: $|E|=\frac{\Delta(N\Phi)}{\Delta t}$ . Lenz: opposes the change: $E=-\frac{d(N\Phi)}{dt}$ . Moving rod: $E=BLv$ .

1. Flux and Faraday's law

\Phi=BA\cos\theta\qquad E=-\frac{\Delta(N\Phi)}{\Delta t}

$\Phi$: flux (Wb = T m²).
$N\Phi$: flux linkage.
$\theta$: angle between $B$ and the normal to the coil.

Worked exampleA collapsing field

200 turns, area $4.0\times10^{-3}$ m², $B$ : 0.50 T → 0 in 0.10 s.

Goal: Average e.m.f.
Strategy: Change in linkage ÷ time.

$\Delta(N\Phi)=200\times0.50\times4.0\times10^{-3}=0.40\text{ Wb}$
Linkage lost.
$E=\frac{0.40}{0.10}=4.0\text{ V}$
Faraday.

Answer

4.0

✓ CheckFaster switch-off gives a bigger e.m.f. ✓.

Moving rod:

E=BLv

$\Delta A=Lv\Delta t$
Area swept by a rod of length $L$ moving at $v$ .
$E=\frac{B\Delta A}{\Delta t}=BLv$
Rate of flux cut.

Worked exampleA sliding rod

0.5 m rod at 4 m s $^{-1}$ across 0.3 T.

Goal: e.m.f.
Strategy: $BLv$ .

$Lv=2\text{ m}^2\text{ s}^{-1}$
Area swept per second.
$E=0.3\times2=0.6\text{ V}$
Flux cut per second.

Answer

0.6

✓ CheckUnits: T m² s

^{-1}

= V ✓.

2. Rotating coil

Flux linkage and induced e.m.f. for a rotating coil

time = 0.0

The e.m.f. is largest when the flux is changing fastest (passing through zero), and zero when the flux is at a maximum.

Common misconceptionFlux vs rate of change Maximum e.m.f. occurs when flux is zero (changing fastest), not maximum.

Pause and think

Why does the magnet fall slowly through copper?

Summary

$E=-d(N\Phi)/dt$ .
Lenz: opposes the change.

Weber: Unit of flux, T m².
Flux linkage: $N\Phi$ .

A coil rotating in a field: flux linkage and induced e.m.f.

By Faraday's law the e.m.f. is minus the gradient of the flux-linkage graph: it is zero when the flux linkage is greatest and largest when the flux linkage passes through zero.

HistoryFaraday's ring. On

29

August

1831

Michael Faraday wound two coils on an iron ring. Switching the current in one made a galvanometer connected to the other twitch, but only at the moment of switching. He'd discovered that it's changing magnetism that makes electricity, the principle behind every generator and transformer.

Fun factInduction hobs. An induction cooker has a coil under the glass carrying alternating current at about

25

kHz. The rapidly changing flux induces eddy currents in the iron pan base, heating it directly. The glass stays relatively cool, and an aluminium pan won't work well.

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