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KVPY Sample Paper KVPY Stream-SX Model Paper-16

  • question_answer
    A square loop of area \[100c{{m}^{2}}\] with sides parallel to X and Y-axes is moved with velocity \[8\,\,cm{{s}^{-1}}\] in positive direction of X-axis. A magnetic field exists in region which points in z-direction. Magnetic field decreases along negative x-direction at rate of \[0.1\,T{{m}^{-1}}\] and also decreases in time at a rate of \[{{10}^{-\,3}}T{{s}^{-\,1}}.\] Emf induced in the loop is

    A) \[10\mu V\]

    B) \[70\mu V\]

    C) \[90\mu V\]

    D) \[100\mu V\]

    Correct Answer: C

    Solution :

    Induced emf, \[E=\frac{d}{dt}{{\phi }_{B}}\] \[=a\int_{0}^{a}{\left( v\frac{\partial B}{\partial x}+\frac{\partial B}{\partial T} \right)}dx\] \[={{a}^{2}}\left( v\frac{\partial B}{\partial x}+\frac{\partial B}{\partial T} \right)\] \[={{(0.1)}^{2}}(0.08\times 0.1\times {{10}^{-\,3}})\] \[=9\times {{10}^{-\,5}}V\] \[=90\mu V\]


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