A 20 cm long metallic rod is rotated with 210 rpm about an axis… | JEE Main 2023 (15 Apr, Shift 1)

Q20JEE Main 2023 · 15 APR · SHIFT 1Easy

Rotating Conductors & AC Generator

A $20\text{ cm}$ long metallic rod is rotated with $210\text{ rpm}$ 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 $0.2\text{ T}$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is ____________ $\text{mV}$ .

Take $\pi = \frac{22}{7}$

Numerical answer type. Work it out, then open the answer.

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Answer: 88

$\omega = \dfrac{2\pi \times 210}{60} = 7\pi = 7 \times \dfrac{22}{7} = 22\text{ rad/s}$
$e = \tfrac{1}{2}B\omega l^2 = \tfrac{1}{2} \times 0.2 \times 22 \times (0.2)^2$
$e = 0.088\text{ V} = 88\text{ mV}$

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