(C) The induced electromotive force (emf) in a conductor rotating in a uniform magnetic field is given by the formula $e = \frac{1}{2} B \omega r^2$,w

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$\frac{1}{2}B\omega ({L^2} + {l^2})$

(C) The induced electromotive force (emf) in a conductor rotating in a uniform magnetic field is given by the formula $e = \frac{1}{2} B \omega r^2$,where $r$ is the effective distance of the end point from the axis of rotation.In this case,the rod is $J$-shaped with segments of lengths $l$ and $L$ perpendicular to each other. The effective distance $r$ from the pivot point $P$ to the other end $Q$ is the straight-line distance,which is $r = \sqrt{l^2 + L^2}$.Substituting this into the formula,we get:$e = \frac{1}{2} B \omega (\sqrt{l^2 + L^2})^2$$e = \frac{1}{2} B \omega (l^2 + L^2)$

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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When a $J$-shaped conducting rod is rotating in its own plane with constant angular velocity $\omega$,about one of its ends $P$,in a uniform magnetic field $\vec B$ directed normally into the plane of the paper,then the magnitude of the emf induced across it will be:

A
$B\omega \sqrt {{L^2} + {l^2}} $
B
$\frac{1}{2}B\omega {L^2}$
C
$\frac{1}{2}B\omega ({L^2} + {l^2})$
D
$\frac{1}{2}B\omega {l^2}$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

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When a $J$-shaped conducting rod is rotating in its own plane with constant angular velocity $\omega$,about one of its ends $P$,in a uniform magnetic field $\vec B$ directed normally into the plane of the paper,then the magnitude of the emf induced across it will be:

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