A 20 cm long metallic rod is rotated with 210 rpm about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field 0.2 T parallel to the axis exists everywhere. The emf developed between the centre and the ring is _________ (Take $π = \frac{22}{7}$ )

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88 mV

22 mV

44 mV

33 mV

answer is A.

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Detailed Solution

The data given is
$ω = 210 \times \frac{2 π}{60} r a d s^{- 1} = 7 π r a d s^{- 1}$
$l = 0.2 m$
$B = 0.2 T$
The emf is given by $ε = \frac{B ω l^{2}}{2} = 0.2 \times 7 π \times \frac{{(0.2)}^{2}}{2} = 88 m V$

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