KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    Two magnets A and B are identical and these are arranged as shown. Their lengths are negligible in comparison to separation between them. A magnetic needle is placed between the magnets at point P and it gets deflected through an angle \[\theta .\] The ratio of distances  and will be

    A) \[{{(2\cot \theta )}^{1/3}}\]

    B) \[{{(2\tan \theta )}^{1/3}}\]

    C) \[(2\cot \theta )\]            

    D) \[{{(2\tan \theta )}^{-1/3}}\]

    Correct Answer: A

    Solution :

    Needle will deflect to magnetic field direction at P
    At P, B is produced by magnet A and B
    B due to magnet \[B={{B}_{1}}\]
    B due to magnet \[A={{B}_{2}}\]
    Formula of B: At axis of magnet \[A=\frac{{{\mu }_{0}}M}{{{d}^{3}}}\]
    At equatorial axis of magnet \[B=\frac{2{{\mu }_{0}}M}{{{d}^{3}}}\]
    \[\therefore {{B}_{2}}=\frac{{{\mu }_{0}}M}{d_{2}^{3}}\]
    \[{{B}_{1}}=\frac{2{{\mu }_{0}}M}{d_{1}^{3}}\]
    \[\tan \,\,(90=\theta )=\frac{{{B}_{2}}}{{{B}_{1}}}\]
    \[\frac{{{B}_{2}}}{{{B}_{1}}}=\cot \theta \]
    \[\frac{1}{2}{{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{3}}=\cot \theta \]
    \[\frac{d}{{{d}_{2}}}={{(2\cot \theta )}^{1/3}}\]

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