Physics 9702 · Paper 4

Spinning Conductors

Rotation is the standard way to change flux forever without running out of field — it is how nearly all mains electricity is generated, and P4 tests it with a wheel.

Spokes and discs sweep circles

A rotating spoke cuts flux like a windscreen wiper: one revolution sweeps the full circle, area πr². Flux cut per revolution Φ = BπR², so the e.m.f. between axle and rim is Φ divided by the period.

A spoke rotating about the axle is a windscreen wiper: in one revolution it sweeps the entire circle, area $\pi R^2$ . So the flux cut per revolution is $B\pi R^2$ , and the e.m.f. between axle and rim is that flux divided by the period.

Worked example

The 2024 wheel

A wheel of rim radius 0.85 m spins at $\omega = 140$ rad s−¹ in a field of 0.18 T along its axis. Find the e.m.f. across one spoke (9702/42/O/N/24 Q1(b)).

Period: $T = 2\pi/\omega = 45\ \text{ms}$ .
Flux cut per revolution: $\Phi = B\pi R^2 = 0.18 \times \pi \times 0.85^2 = 0.41\ \text{Wb}$ .
$E = \Phi/T = 0.41/0.045 = 9.1\ \text{V}$ .

Answer

E \approx 9.1\ \text{V}

A 2023 question ran the same idea on a solid rotating disc at 25 rev/s: flux through the disc 0.069 Wb, e.m.f. between axle and rim $0.069 \times 25 = 1.7$ V (9702/42/M/J/23 Q6(b)).

Generators: why maximum flux means zero e.m.f.

Spin a coil in a field and its flux linkage varies sinusoidally — so by the gradient rule of the last lesson, the e.m.f. is greatest when the coil's plane lies along the field (flux zero, changing fastest) and zero at the moment of maximum flux. Faster rotation raises both the frequency and the peak e.m.f. — the flux changes more often and more quickly. The a.c. this produces is the next chapter's subject.

PreviousFrom Φ–t Graphs to E–t Graphs NextLenz's Law