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 ( $1 G = 10^{- 4} T$ )

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$2.51 \times 10^{- 5} V$

$4.0 \times 10^{- 5} V$

2.51 V

$2.51 \times 10^{- 4} V$

answer is B.

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Detailed Solution

Considering one spoke (OP) as given in diagram.

Induced emf across one spoke (OP),

$\begin{array}{l} e = \frac{{Bωl}^{2}}{2} \\ e = \frac{1}{2} \times 0 .4 \times 10^{- 4} \times 2 π \times (\frac{120}{60}) \times (1)^{2} \\ e = 2 .51 \times 10^{- 4} V \end{array}$

All spokes are parallel to each other, hence net emf

$e_{Net} = e = 2 .51 \times 10^{- 4} V$

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