AC Generator — Rotating Coil in a Magnetic Field

Generator Controls

Rotation speed ω 180°/s

Field strength B 0.60 T

Coil turns N 20

Load resistance R 8.0 Ω

Live Readouts

Φ = N·B·A·cos(ωt)

Instantaneous EMF ε

0.0 V

Peak EMF ε₀ = NBAω

0.0 V

Coil current I = ε/R

0.0 A

Frequency f = ω/2π

0.0 Hz

How it works

A rectangular coil of N turns and area A spins at constant angular velocity ω inside a uniform magnetic field B. As it turns, the flux through the coil changes sinusoidally:

Φ(t)  = N·B·A·cos(ωt)
ε(t)  = -dΦ/dt = N·B·A·ω·sin(ωt)
ε₀    = N·B·A·ω     (peak EMF)
I(t)  = ε(t) / R     (Ohm's law through the load)

ω slider — spin rate of the coil; doubling ω doubles both the frequency and the peak EMF.
B slider — the uniform field strength between the fixed magnet poles; scales the EMF linearly.
N slider — number of turns in the coil; each turn links the same changing flux, so EMF scales linearly with N.
R slider — resistance of the external load circuit; sets how much current flows for a given EMF (I = ε/R) and, through I²R, how much mechanical torque is needed to keep the coil spinning at ω.
The two copper slip rings on the shaft stay in constant sliding contact with fixed carbon brushes, so current can flow continuously out to the external circuit even though the coil itself spins — that's what turns a rotating loop into a usable AC source, and it's exactly how the alternator in a car or a power-station turbogenerator works.

This is the induction half of the Faraday's-law family of phenomena covered on this site: a bar magnet pushed through a static coil produces a single EMF pulse, while a coil rotated continuously in a static field — the mechanism here — produces the sinusoidal alternating voltage that power grids run on.

Coil (induced current) N pole S pole

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