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

  • question_answer
    In a uniform and constant magnetic field of induction B, two long conducting wires ab and cd are kept parallel to each other at distance \[\ell \] with their plane perpendicular to B. The ends a and c are connected together by an ideal inductor of inductance L. A conducting slider wire PQ is imparted a speed \[{{v}_{0}}\] at time t=0. The situation is shown in the figure. At time\[t=\frac{\pi \sqrt{ML}}{4\,B\ell }\], the value of current \[I\] through the wire PQ is (ignore any resistance, electrical as well as mechanical)

    A) \[\sqrt{\frac{mv_{0}^{2}}{L}}\]          

    B) \[\sqrt{\frac{mv_{0}^{2}}{2L}}\]

    C) \[\sqrt{\frac{mv_{0}^{2}}{4L}}\]         

    D) zero

    Correct Answer: B

    Solution :

    [b] \[I(t)=\sqrt{\frac{m}{L}}{{v}_{0}}\,\sin \,\omega t\] where \[\omega =\frac{B\ell }{\sqrt{mL}}\] \[\Rightarrow \,\,I=\sqrt{\frac{mv_{0}^{2}}{2L}}\]


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