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JEE Main & Advanced Physics Electro Magnetic Induction Question Bank Self Evaluation Test - Electromagnetic Induction

  • question_answer
    A conducting wire of mass m slides down two smooth conducting bars, set at an angle 0 to the horizintal as shown in Fig. The separation between the bars is\[l\]. The system is located in the magnetic field B, perpendicular to the plane of the sliding wire and bars. The constant velocity of the wire is   

    A) \[\frac{mg\,R\,\sin \theta }{{{B}^{2}}{{l}^{2}}}\]

    B) \[\frac{mg\,R\,\sin \theta }{B{{l}^{2}}}\]

    C) \[\frac{mg\,R\,\sin \theta }{{{B}^{2}}{{l}^{5}}}\]

    D) \[\frac{mg\,R\,\sin \theta }{B{{l}^{4}}}\]

    Correct Answer: A

    Solution :

    [a] Component of weight along the inclied plane \[=mg\sin \theta \] Again, \[F=BI\ell =B\frac{B\ell v}{R}\ell =\frac{{{B}^{2}}{{\ell }^{2}}v}{R}\] Now, \[\frac{{{B}^{2}}{{\ell }^{2}}v}{R}=mg\,\sin \theta \]  or  \[v=\frac{mgR\,\sin \,\theta }{{{B}^{2}}{{\ell }^{2}}}\]       


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