Question

A wheel with 20 metallic spokes each 1 m long is rotated with a speed of 120 rpm in a plane perpendicular to a magnetic field of 0.4 G. The induced emf between the axle and rim of the wheel will be (1 G = 10^–4 T) 

(1) 2.51 V 

(2) 2.51 × 10^–4 V 

(3) 2.51 × 10^–5 V 

(4) 4.0 × 10^–5 V

Answer 1

Ans: (2) 2.51 × 10^–4 V

Sol. Considering one spoke (OP) as given in diagram.

Induced emf across one spoke (OP),

$e={B\omega l^2\over2}$

$e={1\over2}\times0.4\times10^{-4}\times2\pi\times\left({120\over60}\right)\times1^2$

e = 2.51 × 10^–4 V 

All spokes are parallel to each other, hence net emf 

e_Net = e = 2.51 × 10^–4 V