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A L-shaped conducting rod OAB is rotating in a constant magnetic field of $B_{0} = 100$ Tesla acting along x-axis. The length of rod OA = 20 cm and AB = 20 cm. If rod is rotating about y-axis with constant angular velocity of 5 rad/second then at a given instant.

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Potential difference across OA is 10 Volt

Potential difference across OA is zero Volt

Potential difference across AB is 20 Volt

Potential difference across OB is 10 Volt

answer is B, C.

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Detailed Solution

$d V = (\vec{v} \times \vec{B}) . d \bar{l}$

So potential difference across OA is zero

$\Rightarrow$ Potential difference across $O B = \frac{1}{2} B_{0} ω {(\sqrt{2} O A)}^{2} = \frac{1}{2} (100) (5) 2 {(0.2)}^{2} = 20 V o l t$

So potential difference across AB is also 20 Volt.

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