Flux and flux linkage
For a uniform field, the flux through one turn is Φ = BA cos θ. Flux linkage is NΦ. The readout labelled flux linkage is NBA cos ωt, which is exactly that quantity as the coil turns.
A coil spins at a steady rate in a uniform magnetic field between a north and a south pole. The trace is the induced emf. Change the number of turns N, the field B, the coil area A or the rotation speed, and compare the peak of the trace. Peak emf in this model is NBAω, where ω is the angular speed in radians per second.
For a uniform field, the flux through one turn is Φ = BA cos θ. Flux linkage is NΦ. The readout labelled flux linkage is NBA cos ωt, which is exactly that quantity as the coil turns.
The induced emf equals the negative rate of change of flux linkage: ε = −N dΦ/dt. Differentiating NBA cos ωt gives ε = NBAω sin ωt, so the peak value is NBAω. The simulation plots that sine wave.
The minus sign means the induced current would create a field that opposes the change causing it. In a generator that opposition is why you must keep applying a torque to maintain a steady speed. The trace shows the electrical result; it does not draw the opposing torque.
N, B and A appear once each in NBAω. Rotation speed appears inside ω. Changing one of them, and only one, is the clean way to test the equation against the peak-emf readout.
GCSE and IGCSE introduce electromagnetic induction, Fleming’s right-hand rule and the idea that a faster or stronger change induces a larger emf. A level and IB use Faraday’s law quantitatively for a coil rotating in a uniform field, which is the simple a.c. generator.
The coil is rigid, the field is uniform and the rotation is perfectly steady. Coil resistance, inductance and mechanical losses are not included, so the emf is the ideal induced emf rather than the terminal voltage of a loaded generator.