Rotating Conductors and Generators
Rotating Conductors and Generators
- A spoke rotating through a magnetic field sweeps area continuously. The swept flux per second gives the e.m.f. between axle and rim.
One revolution sweeps one circle
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Symbols
- = magnetic flux cut in one revolution (Wb)
- = revolutions per second (Hz)
- = spoke or disc radius (m)
Worked example
A wheel in a magnetic field
A spoke of radius 0.85 m rotates at 140 rad s⁻¹ in a 0.18 T field perpendicular to the wheel (9702/42/O/N/24 Q1(b)(ii)–(iv)).
- Find the period of one revolution.
- Find the flux cut in one revolution.
- Divide the flux cut by the period.
Answer
Common mistake
A spoke sweeps the whole circular area in one revolution. Do not use the thin physical area of the metal spoke.
Your turnrelationship check
The rotation frequency doubles while field strength and radius remain fixed. State the change in induced e.m.f.
Show worked answer
The induced e.m.f. doubles because the same flux is cut in half the time.
A rotating coil produces alternating e.m.f.
- A rotating coil repeatedly changes its flux linkage, so its induced e.m.f. alternates in direction.
- At maximum flux linkage, the graph is momentarily flat, so e.m.f. is zero.
- At zero flux linkage, the graph is steepest, so e.m.f. magnitude is maximum.
- Faster rotation increases both frequency and maximum e.m.f. The next chapter develops alternating current.
