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KVPY Sample Paper KVPY Stream-SX Model Paper-15

  • question_answer
    A conducting circular loop made of a thin wire, has area \[3.5\times {{10}^{-3}}\,{{\text{m}}^{2}}\] and resistance 10 Ω. It is placed perpendicular to a time dependent magnetic field \[B(t)~=(0.4T)\sin (50\pi t).\] The field is uniform in space. Then the net charge flowing through the loop during \[t=0s\] and \[t=10ms\] is close to:

    A) \[140\,\mu \text{C}\]

    B) \[21\,\mu \text{C}\]

    C) \[6\,\mu \text{C}\]

    D) \[7\,\mu \text{C}\]

    Correct Answer: A

    Solution :

    \[\text{Q}\,=\,\frac{\Delta \phi }{R}\,=\,\frac{1}{10}\text{A}({{\text{B}}_{r}}\,-\,{{\text{B}}_{i}})\] \[=\,\frac{1}{10}\times 3.5\times {{10}^{-3}}\left( 0.4\text{sin}\frac{\pi }{2}\,-\,0 \right)\] \[=\,\frac{1}{10}(3.5\times {{10}^{-3}})(0.4-0)\] \[1.4\times {{10}^{-4}}=\,140\mu \text{C}.\]


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