Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2005

  • question_answer
    In a hydrogen atom an electron moves in a circular orbit of radius \[5.2\times {{10}^{-11}}m\] and produces a magnetic induction of 12.56 T at its nucleus. The current produced by the motion of the electron will be (Given \[{{\mu }_{0}}=4\pi \times {{10}^{-7}}\] Wb/ Am)

    A) \[6.53\times {{10}^{-}}\text{A}\]                             

    B) \[13.25\times {{10}^{-10}}\text{A}\]

    C) \[9.6\times {{10}^{6}}\text{A}\]                               

    D) \[1.04\times {{10}^{-3}}\text{A}\]

    Correct Answer: D

    Solution :

    Magnetic field produced at the centre of circular orbit \[B=\frac{{{\mu }_{0}}}{4\pi }\left( \frac{2\pi I}{r} \right)\]                 or            \[I=\frac{4\pi }{{{\mu }_{0}}}\left( \frac{rB}{2\pi } \right)\]                 Given:   \[r=5.2\times {{10}^{-11}}m,\]                                 \[B=12.56T\]                 So,          \[I=\frac{{{10}^{7}}\times 5.2\times {{10}^{-11}}\times 12.56}{2\times 3.14}\]                                 \[=1.04\times {{10}^{-3}}A\]


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