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Manipal Engineering Manipal Engineering Solved Paper-2012

  • question_answer
    Two points\[A\]and\[B\]are situated at distance\[x\]and\[2x\]respectively from the nearer pole of a magnet\[2\,\,cm\]long. The ratio of magnetic field at\[A\]and\[B\]is

    A)  4 : 1 exactly      

    B)  4 : 1 approximately

    C)  8 : 1 exactly      

    D)         8 : 1 approximately

    Correct Answer: D

    Solution :

    For a magnet\[B=\frac{{{\mu }_{0}}}{4\pi }\frac{2M}{{{r}^{3}}}\,\,\,\,\,\,(nearly)\] \[\Rightarrow \]               \[\frac{{{B}_{2}}}{{{B}_{1}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\] \[\Rightarrow \]               \[\frac{{{B}_{2}}}{{{B}_{1}}}={{\left( \frac{x}{2x} \right)}^{3}}\]   \[\Rightarrow \]    \[\frac{{{B}_{2}}}{{{B}_{1}}}=\frac{1}{8}\] Thus,\[{{B}_{1}}:{{B}_{2}}=8:1\]approximately


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