3.7.5FieldsStretch

Electromagnetic Induction

Push a magnet into a coil of wire and, with no battery anywhere in sight, a current appears. This is $electromagnetic induction$ — the reverse of the motor effect — and it is the working principle behind every generator on the planet, from a bicycle dynamo to a power station turbine.

45 min Video by Science Shorts 3.7.4 Magnetic fields

Electromagnetic Induction, Dynamo Effect & Lenz’s Law — A-level & GCSE PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Define magnetic flux and flux linkage
Use Faraday’s law of electromagnetic induction
State and apply Lenz’s law to find the direction of an induced current
Explain electromagnetic induction in terms of a changing magnetic flux
Describe the basic operation of a simple generator (dynamo effect)

Magnetic flux and flux linkage

$Magnetic flux$ , $Φ$ , through a flat area is the product of the magnetic flux density and the area, when the area is perpendicular to the field (more generally, only the component of $B$ perpendicular to the area counts). For a coil of $N$ turns, each turn links with the same flux, so the total $flux linkage$ is $N Φ$ — it is flux $linkage$ , not flux alone, that determines the induced e.m.f. in a coil.

Φ = B A flux linkage = N Φ

Magnetic flux (for B perpendicular to area A) and flux linkage through N turns.

1Flux:

Φ = B A = 0.30 \times 0.0050 = 1.5 \times 1 0^{- 3}

Wb.

2Flux linkage:

N Φ = 200 \times 1.5 \times 1 0^{- 3}

AnswerFlux linkage

= 0.30

Wb-turns

Faraday’s law

$Faraday’s law$ of electromagnetic induction states that the induced e.m.f. in a circuit is equal to the rate of change of flux linkage through it. An e.m.f. (and hence a current, if the circuit is closed) is only induced while the flux linkage is $changing$ — a steady, unchanging flux, however large, induces nothing at all.

Flux linkage can change for several reasons: the magnetic field strength changing, the area of the coil changing, the coil rotating relative to the field (changing the effective perpendicular area), or the coil (or magnet) simply moving so the flux through it changes.

ε = - \frac{Δ ( N Φ )}{Δ t}

Faraday’s law: induced e.m.f. = rate of change of flux linkage (the minus sign encodes Lenz’s law).

1Change in flux linkage:

Δ (N Φ) = 0.060 - 0.020 = 0.040

Wb-turns.

2Use

ε = \frac{Δ ( N Φ )}{Δ t}

(magnitude only).

ε = \frac{0.040}{0.50}

Answer

ε = 0.080

Tip — A bigger coil (more turns, N) or a faster rate of change both increase induced e.m.f. — this is why generators spin their coils quickly and use many turns of wire.

Lenz’s law

$Lenz’s law$ states that the direction of an induced current is always such that it opposes the change that produced it — encoded by the minus sign in Faraday’s law. If a magnet is pushed into a coil, the induced current creates its own magnetic field that pushes back against the approaching magnet (rather than helping it in); pulling the magnet back out induces a current in the opposite sense, this time trying to attract the magnet back.

Lenz’s law is ultimately a statement of $conservation of energy$ : if the induced current instead $assisted$ the change (attracting an approaching magnet, say), it would accelerate the process, generating ever more current and energy from nothing — a violation of energy conservation that never happens.

Tip — A quick check for Lenz’s law questions: whatever it is that’s changing (a magnet approaching, a field increasing), the induced effect always tries to resist that specific change.

The dynamo effect and simple generators

A simple generator (dynamo) rotates a coil within a magnetic field (or, equivalently, rotates a magnet near a fixed coil). As the coil turns, the flux linkage through it constantly changes — maximal when the coil is edge-on to the field and rotating fastest through the field lines, zero when the coil is flat-on to the field, momentarily not rotating "through" any lines — producing an alternating (sinusoidal) e.m.f. that reverses direction twice per rotation.

The direction of the induced current at any instant is found using $Fleming’s right-hand rule$ (the generator-effect counterpart to the left-hand rule for motors): thu $M$ b = $M$ otion of the conductor, $F$ irst finger = $F$ ield, se $C$ ond finger = induced $C$ urrent.

Tip — Motor effect (force from current): LEFT hand. Generator effect (current from motion): RIGHT hand. Keep the two straight — they are mirror-image rules for reverse processes.

Equation recap

Φ = B A

Magnetic flux through an area perpendicular to B.

flux linkage = N Φ

Flux linkage through N turns.

ε = - \frac{Δ ( N Φ )}{Δ t}

Faraday’s law of electromagnetic induction.

Common mistakes to avoid

Thinking a large, constant magnetic flux through a coil induces a large e.m.f.

Faraday’s law depends on the RATE OF CHANGE of flux linkage — a constant flux, however large, induces nothing at all.

Assuming Lenz’s law and Faraday’s law are two unrelated rules.

Lenz’s law is encoded directly in the minus sign of Faraday’s law — the induced e.m.f. always acts to oppose the change producing it.

Mixing up Fleming’s left-hand rule (motor effect) and right-hand rule (generator effect).

LEFT hand finds the force from a current (motor effect); RIGHT hand finds the induced current from motion (generator/dynamo effect) — they are reverse processes needing different hands.

Key takeaways

Magnetic flux Φ = BA; flux linkage through a coil of N turns = NΦ.
Faraday’s law: induced e.m.f. = rate of change of flux linkage, ε = −Δ(NΦ)/Δt.
Lenz’s law: the induced current always opposes the change producing it — a consequence of conservation of energy.
A rotating coil in a field (a simple generator) produces an alternating e.m.f.; use Fleming’s right-hand rule to find induced current direction.

Test yourself

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Electromagnetic Induction

Push a magnet into a coil of wire and, with no battery anywhere in sight, a current appears. This is

electromagnetic induction

— the reverse of the motor effect — and it is the working principle behind every generator on the planet, from a bicycle dynamo to a power station turbine.

45 min Video by Science Shorts 3.7.4 Magnetic fields