UPSEE Solved Model Paper 2

Refer to Fig. Let v be the frequency of rotation.
The time taken for 1 full rotation is T = 1/v.
Therefore, rate of change of area is

A

T

=

πr2

T

= πr2v
Now, the emf induced between the axle and rim is e = B × rate of change of area
= B×πr2v =

1

2

Br2ω (Since ω = 2πv)
Since the same emf is produced between the ends of each spoke, and these emfs are in parallel as is evident from Fig. The net emf between the axle and the rim of the wheel will be the same as that across each spoke. We notice that all the eight spokes are connected with one end at the rim and the other at the axle. Hence the magnitude of the net emf between the axle and the rim is independent of the number of spokes.