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JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Electromagnetic Induction

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}

Answer: 88

Solution

The angular speed is

ω = 210 rpm = 210 \times \frac{2 π}{60} = 7 π rad s^{- 1}

. A rod rotating about one end in a field parallel to the axis develops

ε = \frac{1}{2} B ω ℓ^{2}

. Substituting with

π = \frac{22}{7}

,

ε = \frac{1}{2} \times 0.2 \times 7 π \times (0.2)^{2} = 0.088 V

, so the emf between the centre and the ring is

88 mV

.

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Integer answer

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