Electromagnetic Induction

Oersted showed a current makes a magnet. Faraday asked the reverse: can a magnet make a current? Plunge a magnet into a coil and watch the galvanometer twitch — that twitch is the seed of every generator, transformer, and motor below. Same idea, eight acts, one thread.

Act 1 · Faraday's Law of Induction

Plunge a magnet into a coil, and the coil pushes back with a current

Faraday connected a coil to a sensitive galvanometer and plunged a bar magnet in and out. Each time the magnet moved, the needle twitched — one way going in, the opposite way coming out. No motion, no twitch. The induced emf only exists while the magnetic flux linked with the coil is changing.

S N G coil linked with a moving bar magnet
emf = -N Δφ/Δt = 0 V
Speed, v0.40 m/s
Faster motion, faster flux change, bigger twitch.
Turns, N50
More turns, more emf for the same flux change.

The needle always swings to oppose whatever caused it. That opposition has a name: Lenz's rule.

Act 2 · Lenz's Rule & Fleming's Right-Hand Rule

The induced current always fights the change that made it

As the magnet's north pole approaches the coil, the induced current forms a north pole at the near end to repel it — resisting the approach. Pull the magnet away, and the coil flips to a south pole to attract it back — resisting the departure. Either way, the coil fights the change.

N G S N repels the approaching magnet thumb: motion forefinger: field middle: current Fleming's right-hand rule

Point the right thumb along the wire's motion and the forefinger along the field — the middle finger gives the induced current's direction.

Act 3 · Induced EMF in a Moving Straight Wire

Slide a rod across a field and its free charges feel a sideways push

A rod of length ℓ slides with velocity v across a uniform field B. The charges inside the rod are dragged along with it and feel a magnetic force that sweeps them to one end, building up an emf = Bℓv sinθ between the rod's ends.

G v field into the page (×), rod free to slide along the rails
emf = Bℓv sinθ = 0 V
Flux density, B0.80 T
Rail spacing, ℓ0.30 m
Velocity, v0.50 m/s
Angle, θ90°
emf peaks at 90° and vanishes when v runs parallel to B.

Now instead of sliding a straight rod, spin a whole loop through the field — and you've built a generator.

Act 4 · Mutual Induction Between Two Coils

A changing current in one coil induces an emf in its neighbor

No wires touch, yet the secondary coil feels every change in the primary's current. As the primary's current rises or falls, its flux washes over the secondary and induces an emf there — proportional to the rate of change and to how tightly the two coils are coupled, M.

primary (battery + rheostat) G secondary
emf = -M ΔI₁/Δt = 0 V
Mutual inductance, M0.10 H
Iron core, more turns, or closer coils all raise M.
Rate of change, ΔI₁/Δt20 A/s
Positive: primary current rising. Negative: falling.

Even a single coil feels this effect from its own changing current — that's self-induction.

Act 5 · Self-Induction & Eddy Currents

A coil resists changes in its own current — sometimes violently

Open the switch on a large electromagnet coil and its current tries to keep flowing. The collapsing flux induces a huge emf in the coil itself (self-induction), large enough to jump a spark across the switch or light a neon bulb that needs about 180 V to fire.

switch V neon lamp
emf = -L ΔI/Δt = 0 V
Self-inductance, L2.0 H
Steady current, I1.5 A
Open the switch above to collapse it and watch the spark.
eddy currents in a solid conductor (heating → induction furnaces)
Rate of flux changeMedium

Spin a coil continuously through a field instead of just plunging a magnet, and the induction never stops — that's a generator.

Act 6 · The AC Generator (Dynamo)

A coil spinning in a field produces an emf that rises and falls like a wave

A coil of N turns and area A rotates at angular speed ω between the poles of a magnet. The emf peaks when the coil's plane runs parallel to the field (cutting flux fastest) and vanishes when it's perpendicular — tracing a perfect sine wave once per revolution.

N S slip rings & brushes emf vs. angle (one revolution)
emf = NBAω sinθ = 0 V · (emf)max = 0 V
Turns, N100
Flux density, B0.20 T
Coil area, A0.05 m²
Frequency, f50 Hz
f is the number of full oscillations per second; home power runs at 50 Hz.

Swap the slip rings for a split-ring commutator, and the same spinning coil delivers current in one direction only.

Act 7 · Rectification & the DC Motor

Split the rings in two, and alternating current becomes one-directional

Replace the two continuous slip rings with a single ring split into two insulated halves (a commutator). Each half swaps which brush it touches exactly when the coil's emf passes through zero, so the external circuit always sees current flowing the same way — a bumpy but unidirectional "DC". Run the same machine backwards — feed it a battery instead of reading a meter — and the coil spins: that's a DC motor, steered by Fleming's left-hand rule instead of the right.

AC output (slip rings)

In the motor, current from the battery passes through the coil in the field; Fleming's left-hand rule (thumb = force, forefinger = field, middle = current) gives the torque direction that keeps it turning, half a revolution at a time as the commutator flips the connection.

Two coils linked by a shared iron core, and mutual induction becomes a practical machine: the transformer.

Act 8 · The Transformer

Mutual induction, packaged to step voltage up or down

An AC primary current builds a changing flux that an iron core funnels entirely through the secondary coil. The voltage ratio follows the turns ratio exactly; the current ratio runs the other way, so power in roughly equals power out.

primary, Nᶧ secondary, Nₛ step-up transformer
Vₛ/Vᶧ = Nₛ/Nᶧ  ·  Iₛ/Iᶧ = η·Nᶧ/Nₛ
Vᶧ = 220 V  Iᶧ = 1.0 A  Vₛ = 0 V  Iₛ = 0 A
Primary turns, Nᶧ1000
Secondary turns, Nₛ2000
Primary voltage, Vᶧ220 V
Efficiency, η90%
Real transformers lose a little to wire resistance and eddy currents in the core.

Step the voltage up for transmission (small current, small I²R loss over the long wires), then step it back down near your home — 220 V, ready for the wall socket.

In a nutshell
  • Faraday's law: emf = -NΔφ/Δt — only a changing flux induces an emf.
  • Lenz's rule: the induced current always opposes the change that produced it.
  • Fleming's right-hand rule: thumb = motion, forefinger = field, middle finger = induced current.
  • Motional emf: emf = Bℓv sinθ for a rod sliding through a field.
  • Mutual induction: emf = -MΔI₁/Δt — one coil's changing current induces emf in another.
  • Self-induction: emf = -LΔI/Δt — a coil resists changes in its own current; the henry is the unit of L and M.
  • AC generator: emf = NBAωsinθ, maximum NBAω — a spinning coil traces a sine wave.
  • Commutator: splits the slip ring so the output current never reverses — a (bumpy) DC generator; reversed, the same machine is a DC motor.
  • Transformer: Vₛ/Vᶧ = Nₛ/Nᶧ, Iₛ/Iᶧ = Nᶧ/Nₛ (ideal); η = output power / input power.