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

  • question_answer
    A conducting rod of mass m and \[\ell \]is placed on a smooth horizontal surface in a region where transverse uniform magnetic field B exists in the region. At t=0, constant force .F starts acting on the rod at its mid-point as shown. Potential difference between ends of the rod, \[{{V}_{p}}-{{V}_{Q}}\] at any time t is     

    A) \[\frac{BF\ell t}{2m}\]

    B) \[\frac{BF\ell t}{4m}\]

    C) \[\frac{5BF\ell t}{8m}\]

    D) \[\frac{7BF\ell t}{8m}\]

    Correct Answer: A

    Solution :

    [a] Velocity at any time t,    \[v=a\] \[t=\frac{F}{m}t\] Now, \[e={{V}_{P}}-{{V}_{Q}}=Bv\ell \,\sin \,{{30}^{o}}=B\left( \frac{Ft}{m} \right)\ell \times \frac{1}{2}\] \[=\frac{BF\ell t}{2m}\]


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