A rod of length \( 2 a \) is free to rotate in a vertical plane, about a horizontal axis \( O \)...

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A rod of length \( 2 a \) is free to rotate in a vertical plane, about a horizontal axis \( O \) passing through its mid-point. A long straight, horizontal wire is in the same plane and is carrying a constant current \( i \) as shown in figure. At initial moment of time, the rod is horizontal and starts to rotate with constant angular velocity \( \omega \), calculate emf induced in the rod as a function of time.
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