Diagrams.ink / Electromagnetic induction

A turning coil makes alternating voltage

Crank the coil between the magnet's poles. Voltage does not follow how much field passes through the coil. It follows how fast that flux is changing, and that is why it is zero when the coil is face-on.

Fig. 07  Idealised AC generatorStarting
1 2 3 4 5 6 ↻ Drag to turn the crank
1N and S polesField runs N → S (blue lines)
2Coil, 3 turnsLit lines pass through it = flux
3Slip ringsEach coil end has its own ring
4Carbon brushesStay still, touch the rings
5LampThe outside circuit
6CrankDrag it, or use the motor

Coil angle

0°0° = face-on to the field

Flux through coil

+100%of its maximum, Φ = Φmax cos θ

Voltage now

0.0 Ve = peak × sin θ

Frequency

0.50 Hzone cycle per turn

Peak voltage

3.0 Vproportional to speed

Voltage and flux, linked to the coil angle

Voltage e (V)Flux Φ (% of max)
The marker sits at the coil's angle. Try holding the coil at 0° or 90° with the crank, then spin faster: the shape stays put, only its height grows.

Induction

A changing magnetic flux through a loop pushes charge around it. Faraday's law: e = −dΦ/dt. Flux through the coil is Φ = B·A·cos θ, so turning the coil changes Φ continuously and makes a voltage.

Zero at the flux extremes

At 0° and 180° the coil faces the field squarely and Φ is largest (or most negative). It is at the top of its curve, so for an instant it is not changing, and the sides move along the field lines, cutting none. Voltage is zero. At 90° and 270° Φ is zero but changing fastest: peak voltage.

Speed: frequency and amplitude

Turning twice as fast makes each cycle take half as long, so frequency doubles. It also changes the flux twice as fast, so the peak voltage doubles: e = Φmax·ω·sin θ. Reverse the rotation and the same curve is flipped.

Idealised model. Uniform field, a rigid coil turning at the speed shown, no resistance, no inductance and no braking force from the current. The lamp only visualises e². Numbers are illustrative: full scale is 12 V at 2 turns/s. Slip rings let the brushes keep touching the same coil end, so the lamp sees the voltage change sign each half turn. A split-ring commutator would swap the connections to make it one-way.