Faraday's Law Calculator
Faraday's law calculator finds the voltage induced in a closed circuit.
Induced EMF2.5 V−N dΦ/dt. The MINUS sign is Lenz's law: the induced current opposes the change that made it, which is energy conservation rather than a separate rule
Flux change per turn2.5 mWbarea × the change in flux density
Total flux linkage change250 mWbN times as much, which is why coils have many turns
Rate of change of flux density5 T/s
What matters is the RATEnot the field strengtha steady field of any strength induces nothing at all. Holding a magnet still inside a coil produces no EMF whatever, however powerful the magnet
Motional EMF2.5 VBLv for a conductor of 0.5 m sweeping at 10 m/s — the same law, seen from the conductor's point of view rather than the circuit's
Peak EMF from a rotating coil39.26991 VNBAω at 1,500 rpm — this is a generator, and the output is sinusoidal because the flux linkage varies as the cosine of the angle
RMS EMF27.76802 Vpeak divided by √2
Output frequency25 Hzone cycle per revolution for a two-pole machine
The formula
ε = −N dΦ/dt; ε = BLv; ε_peak = NBAω
The rate is everything
Faraday's law says the induced EMF depends on how fast the flux changes, not on how much flux there is. A stationary magnet inside a coil induces nothing at all, however strong it is. Moving a weak magnet quickly beats holding a strong one still.
The minus sign is Lenz's law, and it is not an extra rule bolted on — it is energy conservation. If the induced current reinforced the change that produced it, the system would accelerate itself and generate energy from nothing. The opposition is why a generator gets harder to turn as you draw more current from it, and why dropping a magnet down a copper pipe takes so long.