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Manipal Medical Manipal Medical Solved Paper-2006

  • question_answer
    A plane metallic sheet is placed with its face parallel to lines of magnetic induction B of a uniform field. A particle of mass m and charge q is projected with a velocity\[v\]from a distance \[d\]from the plane normal to the lines of induction. Then, the maximum velocity of projection for which the particle does not hit the plate is:

    A)  \[\frac{2Bqd}{m}\]

    B)  \[\frac{Bqd}{m}\]

    C)  \[\frac{Bqd}{2m}\]

    D)  \[\frac{Bqm}{d}\]

    Correct Answer: B

    Solution :

     The charged particle bends in a circle of radius r. \[Bqv\sin \frac{\pi }{2}=\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \] \[r=\frac{mv}{Bq}\] The particle does not hit the plate if \[r\le d\] Or \[\frac{mv}{Bq}\le d\] Or \[v\le \frac{Bqd}{m}\] \[\therefore \] \[{{v}_{\max }}\le \frac{Bqd}{m}\]


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