Rule of thumb · PhysicsNº 89 / 238

A coil turning in a magnetic field makes a peak voltage of N times B times A times its angular speed

How much voltage does a spinning coil make?

A coil of N turns and area A turning in a field B makes a sine wave of peak voltage N B A times its angular speed in radians a second, so 100 turns of 100 cm² turning at 50 revolutions a second in 0.1 T peak at 31 V, which a meter reads as 22 V.

Why it works

The voltage is minus the turns times the rate of change of the flux (Faraday’s law), and the flux through a turning coil is B A cos ωt, so the voltage is N B A ω sin ωt. The RMS value, what a meter or a heater sees, is the peak divided by √2. The frequency is the rate of turning: 3,000 rpm gives 50 Hz with one pair of poles, 3,600 rpm 60 Hz.

When it fails

It is the open-circuit voltage of an ideal coil in a uniform field. A load draws current, which loses voltage in the winding and makes a field that opposes the turning, so a real generator makes less, and iron in the machine saturates. The winding’s own inductance rounds the wave.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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