A 20 cm long metallic rod is rotated with 210 rpm about an axis normal to the rod passing through its one end. [2023]

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Solution

Q.
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 _________ mV. Take $π = \frac{22}{7}$ . [2023]

Ans.
(88)

$Here ω = 210 rpm = 210 \times \frac{2 π}{60} rad.s$

$\Rightarrow ω = 7 π rad/s. and l = 0.2 m$

$and B = 0.2 T$

$emf developed across rod is = \frac{1}{2} B ω l^{2}$

$\frac{1}{2} \times 0.2 \times 7 π \times {(0.2)}^{2} = 88 mV$

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