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.
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.
The needle always swings to oppose whatever caused it. That opposition has a name: Lenz's rule.
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.
Point the right thumb along the wire's motion and the forefinger along the field — the middle finger gives the induced current's direction.
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.
Now instead of sliding a straight rod, spin a whole loop through the field — and you've built a generator.
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.
Even a single coil feels this effect from its own changing current — that's self-induction.
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.
Spin a coil continuously through a field instead of just plunging a magnet, and the induction never stops — that's a generator.
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.
Swap the slip rings for a split-ring commutator, and the same spinning coil delivers current in one direction only.
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.
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.
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.
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.