question_answer

A conducting rod of length L and mass m is moving down a smooth inclined plane of inclination 0 with constant speed v. A current I is flowing in the conductor perpendicular to plane of paper (inwards). A vertically upward uniform magnetic field B exists in space there. The magnitude of magnetic field is

A) \[\frac{mg}{IL}\sin \theta \]                       

B) \[\frac{mg}{IL}\cos \theta \]

C) \[\frac{mg}{IL}\tan \theta \]                      

D) \[\frac{mg}{IL}\sec \theta \]

Correct Answer: C

Solution :

As the conductor is moving with constant velocity net force acting on it must be zero. forces acting on conductor are magnetic force, gravity force & contact force as shown. For dynamic equilibrium ,\[mg\sin \theta =lBl\cos \theta \]\[\Rightarrow \]\[B=\frac{mg\tan \theta }{lL}\]