AC Generator EMF Calculator (Faraday's Law)
Peak, RMS and instantaneous voltage of a coil spinning in a magnetic field, with the sine wave drawn over two turns.
Results
Peak EMF
62.8319
V
RMS EMF
44.4288
V
EMF at that instant
44.4288
V
Peak flux linkage N·B·A
0.2
Wb
Rotation speed
3000
rpm
The dashed line marks the value you entered.
What this tool does
Faraday's law of induction — the third of Maxwell's equations — says a changing magnetic flux through a coil drives a voltage around it. Spin a coil of N turns in a steady field and the flux swings between +NBA and −NBA every turn, giving a sine wave whose peak is N·B·A·ω. The peak grows with speed, which is exactly why a bicycle dynamo gives a dim light when you ride slowly. Real generators add iron cores and several pole pairs, but the sine and its peak come from this same line.
Formula
e(t) = N B A ω sin(ωt) · ω = 2πf · E_peak = N B A ω · E_rms = E_peak ÷ √2
Variables
| Symbol | Meaning | Unit |
|---|---|---|
nt | Number of turns | — |
b | Magnetic field | mT |
a | Coil area | cm² |
f | Rotation frequency | Hz |
t | Instant | ms |
EP | Peak EMF | V |
ER | RMS EMF | V |
ET | EMF at that instant | V |
FL | Peak flux linkage N·B·A | Wb |
RPM | Rotation speed | rpm |
Worked example
- Number of turns100
- Magnetic field200 mT
- Coil area100 cm²
- Rotation frequency50 Hz
- Instant2.5 ms
- Peak EMF62.8319 V
- RMS EMF44.4288 V
- EMF at that instant44.4288 V
- Peak flux linkage N·B·A0.2 Wb
- Rotation speed3000 rpm
Limitations
- The formula assumes ideal geometry — an infinitely long wire or coil, a perfectly uniform sphere — in empty space or a uniform material. Real parts come close, but ends, nearby metal and magnetic materials change the field.
- Electrical installations are governed by national wiring rules. Cable sizing also depends on installation method, grouping, ambient temperature and protection devices, which this calculator does not evaluate.