A rod of length l,mass m,and resistance R sli | vedclass

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(C) The motional $emf$ induced in a conductor of length $l$ moving with velocity $v$ in a magnetic field $B$ is given by the formula $\varepsilon = \v

Vedclass · Accepted Answer

$B\,l\,v\,\cos\,	heta$

Vedclass · Answer

(C) The motional $emf$ induced in a conductor of length $l$ moving with velocity $v$ in a magnetic field $B$ is given by the formula $\varepsilon = \vec{v} \cdot (\vec{B} 	imes \vec{l})$.Alternatively,the magnitude of induced $emf$ is $\varepsilon = B_{\perp} l v$,where $B_{\perp}$ is the component of the magnetic field perpendicular to the plane of the motion of the rod.In this case,the rod is moving down an inclined plane making an angle $	heta$ with the horizontal.The magnetic field $B$ is vertical.The component of the magnetic field perpendicular to the inclined plane is $B \cos 	heta$.The length of the rod $l$ is perpendicular to the velocity $v$ and also perpendicular to the component $B \cos 	heta$.Therefore,the induced $emf$ is $\varepsilon = (B \cos 	heta) l v = B l v \cos 	heta$.

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