Question

A cycle wheel with 64 spokes is rotating with $N$ rotations per second at right angles to the horizontal component of the magnetic field. The induced emf generated between its axle and rim is $E$. If the number of spokes is reduced to 32 then the value of induced emf will be:
a) $E$
b) $2E$
c) $\dfrac{E}{2}$
d) $\dfrac{E}{4}$

Answer 1

Hint: Here, emf is induced between the axle and the rim of the cycle. The number of spokes in the cycle holds minimum importance in such regard. We need to analyze the change within the axle and rim with the number of spokes present in the cycle.

Complete answer:
The emf induced between the axle and the rim is $E$. Here the emf induced is $E$ in every spoke of the cycle.
Hence, increasing or decreasing the number of spokes, although may change the overall emf induced in the cycle but the emf induced in each spoke remains the same irrespective of the number of spokes present in the cycle.
Hence, the emf induced in each spoke of the cycle, from axle to rim, with the cycle containing 32 spokes is $E$.
Thus, the answer is option (a).

Additional information:
Emf is induced whenever there is a relative motion between the magnetic field and the conductor. The induced emf is directed in such a way that it opposes its cause of generation. This is called the Faraday’s Law of Electromagnetic Induction. The emf induced in each conductor crossing the magnetic field depends upon the velocity and the length of each conductor rather than the number of conductors itself.

Note: The number of spokes do not have any impact on the amount of emf Induced in each spoke. The emf induced only depends upon the speed and the length of each spoke. Thus, even if we increase or decrease the number of spokes, the emf induced in each spoke will remain the same.