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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2007

  • question_answer
    A and B are two concentric circular conductors of centre 0 and carrying currents \[{{\text{I}}_{\text{1}}}\]and \[{{\text{I}}_{2}}\] as shown in the figure. The ratio of their radii is 1: 2 and ratio of the flux densities at 0 due to A and B is 1 : 3.The value of \[{{\text{I}}_{1}}\text{/}{{\text{I}}_{2}}\]will be

    A)  1/6                                       

    B)  ¼

    C)  1/2                                       

    D)  1/3

    Correct Answer: A

    Solution :

    Magnetic field produced at the centre by loops, \[{{B}_{1}}=\frac{{{\mu }_{0}}{{I}_{1}}}{2{{r}_{1}}},\]       s\[Bl2=\frac{{{\mu }_{0}}{{I}_{2}}}{2{{r}_{2}}}\]                 \[\frac{{{B}_{1}}}{{{B}_{2}}}=\frac{{{I}_{1}}}{{{I}_{2}}}\times \frac{{{r}_{2}}}{{{r}_{1}}}\] But given   \[\frac{{{B}_{1}}}{{{B}_{2}}}=\frac{1}{3}\] \[\therefore \]  \[\frac{1}{3}=\frac{{{I}_{1}}}{{{I}_{2}}}\times \frac{2}{1}\] \[\therefore \]  \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{1}{6}\]


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