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A conducting rod (OP) of length L rotates in the form of a conical pendulum with an angular velocity $ω$ about a fixed vertical axis passing through its end O. There is a uniform magnetic field B in vertically downward direction. The rod makes an angle $θ$ with the direction of the magnetic field. The emf induced across the ends of the rod is

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$\frac{B ω L^{2} \cos^{2} θ}{2}$

$\frac{B ω L^{2} \tan^{2} θ}{2}$

$\frac{B ω L^{2}}{2}$

$\frac{B ω L^{2} \sin^{2} θ}{2}$

answer is A.

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Detailed Solution

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$V = x ω \sin θ$

$d e = B v d x \sin θ$

$e = \int_{0}^{l} B v d x \sin θ$

$= \frac{1}{2} B ω \sin^{2} θ l^{2}$

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