A coil with N=100, B=0.5T, A=0.01m² spins at 60Hz. What is the peak EMF?

Ε_max = NBAω = 100 × 0.5 × 0.01 × 2π×60 ≈ 188 V.

Why does the EMF vary as sin(ωt) and not cos(ωt)?

It depends on the starting angle — 0° at t=0 when coil is parallel to field gives sin.

Why do wind turbines use permanent magnet generators instead of electromagnets?

Permanent magnets need no excitation power and work even when grid is down.

Pro 🔒~20 min

Generator

Convert mechanical energy to electrical energy

How it works

An electric generator converts mechanical energy to electrical energy by rotating a coil in a magnetic field. The changing magnetic flux induces an alternating EMF proportional to the number of turns N, field strength B, coil area A, and angular velocity ω. This is the reverse of a motor. The output frequency equals the rotation frequency — 60 Hz for US power grids requires 3600 rpm (or 1800 rpm with 4-pole machines).

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Step-by-step

Adjust the rotation speed slider and observe the AC output on the oscilloscope.
Increase field strength or coil turns to boost the peak voltage.
Switch to motor mode — now the external AC drives rotation instead.

Key formulas

$\mathcal{E}(t) = NBA\omega\sin(\omega t)$ Generator EMF
$\omega = 2\pi f$ Angular frequency
$\mathcal{E}_{max} = NBA\omega$ Peak EMF

Frequently asked questions

A coil with N=100, B=0.5T, A=0.01m² spins at 60Hz. What is the peak EMF?: Ε_max = NBAω = 100 × 0.5 × 0.01 × 2π×60 ≈ 188 V.
Why does the EMF vary as sin(ωt) and not cos(ωt)?: It depends on the starting angle — 0° at t=0 when coil is parallel to field gives sin.
Why do wind turbines use permanent magnet generators instead of electromagnets?: Permanent magnets need no excitation power and work even when grid is down.