Two wheels containing \( 100 \) and \( 50 \) iron spokes of same length, respectively, are rotating with same angular speed in a plane normal to a uniform magnetic field of \( 1 \) G. The ratio of induced emfs between axle and rim of wheels respectively, is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1:1 \)
A spoke of length \( l \) rotating about one end with angular speed \( \omega \) in a perpendicular field has a motional emf between its ends:
\( \displaystyle \varepsilon = \int_{0}^{l} B\omega r\,dr = \frac{1}{2}B\omega l^{2} \)
Each spoke connects the axle to the rim, so all the spokes are in parallel between the axle and the rim, like identical cells in parallel. The emf between the axle and the rim is therefore that of one spoke, whatever the number of spokes.
With the same \( B \), \( \omega \) and \( l \) for both wheels:
\( \varepsilon_1:\varepsilon_2 = 1:1 \)
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Motional Electromotive Force – “… Example 6.7 A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of earth’s magnetic field HE at a place. If HE = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? … The number of spokes is immaterial because the emf’s across the spokes are in parallel.”