2. Sample Papers
  3. KVPY

KVPY Sample Paper KVPY Stream-SX Model Paper-31

  • question_answer
    A rigid circular loop of radius r and mass m lies in the x-y plane on a flat table and has a current i flowing in it. At this particular place, the earth's magnetic field is \[\overrightarrow{B}={{B}_{x}}\overset{\hat{\ }}{\mathop{i}}\,+{{B}_{z}}\overset{\hat{\ }}{\mathop{k}}\,\] The value of i so that one edge of the loop lifts from the table 's:

    A) \[\,\frac{mg}{\pi r\sqrt{B_{x}^{2}+B_{z}^{2}}}\]

    B) \[\frac{mg}{\pi r{{B}_{z}}}\]

    C) \[\frac{mg}{\pi r{{B}_{x}}}\]

    D) \[\frac{mg}{\pi r\sqrt{{{B}_{x}}{{B}_{z}}}}\]

    Correct Answer: C

    Solution :

    The torque on the loop must be equal to the gravitational torque exerted about an axis tangent to the loop.
    The gravitational torque:
    \[{{\tau }_{1}}=mgr\]                ...(1)
    Only \[{{B}_{x}}\], causes a torque. Therefore torque to the magnetic field
    \[{{\tau }_{2}}=\left| \overrightarrow{M}\times \overrightarrow{B} \right|=MB\sin 90{}^\circ =\pi {{r}^{2}}i{{B}_{x}}\] ...(2)
    Eqs.(1) and (2),we get, \[i=\frac{mg}{\pi r{{B}_{x}}}\]
     


You need to login to perform this action.
You will be redirected in 3 sec spinner