A metal rod moves at a constant velocity in a | vedclass

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(B) When a metal rod of length $l$ moves with a velocity $v$ in a uniform magnetic field $B$ perpendicular to both the length of the rod and the veloc

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There is an electric field in the rod.

Vedclass · Answer

(B) When a metal rod of length $l$ moves with a velocity $v$ in a uniform magnetic field $B$ perpendicular to both the length of the rod and the velocity,a motional electromotive force (emf) is induced across the ends of the rod.According to the Lorentz force law,the free electrons in the rod experience a magnetic force $F_m = q(v 	imes B)$. Due to this force,electrons accumulate at one end of the rod,creating a potential difference between the ends.This separation of charge creates an internal electric field $E$ within the rod,which exerts an electric force $F_e = qE$ on the charges,opposing the magnetic force.At equilibrium,the magnetic force is balanced by the electric force,i.e.,$qE = qvB$,which implies $E = vB$.Since an electric field $E$ exists within the rod,the potential varies along the length of the rod. Therefore,statement $(b)$ is correct.

$A$ metal rod moves at a constant velocity in a direction perpendicular to its length. $A$ constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement$(s)$ from the following.

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