Discussion
A wheel with 10 metallic spokes each 0.5 m long is rotated with speed 120 revolutions/minute in a plane normal to horizontal component of Earth's magnetic field HE at a place. If HE = \(4 \times 10^{-5}\) T is at the place, what will happen to emf induced between axle and rim of wheel if same wheel has double metallic spokes ?
Answer: A
The induced emf remains the same.
Each spoke rotating in the field has the same emf \(\frac{1}{2}B\omega l^{2}\) between the axle and the rim, and all the spokes connect the axle to the rim side by side, that is, in parallel. Connecting identical emfs in parallel does not change the voltage, so the emf between axle and rim depends only on B, the angular speed and the spoke length.
Doubling the number of spokes therefore leaves the emf unchanged (it would only lower the internal resistance). The emf would double only if the spokes were in series, which they are not.
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