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CET Karnataka Medical CET - Karnataka Medical Solved Paper-2010

  • question_answer
    An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is\[\sigma \]. Electric intensity in the space between the plates is E. A uniform magnetic field B also exists in the space perpendicular to the direction of E. The electron moves perpendicular to both \[\overset{\to }{\mathop{\mathbf{E}}}\,\]and \[\overset{\to }{\mathop{\mathbf{B}}}\,\]without any change in direction. The time taken by the electron to travel a distance I in the space is

    A)  \[\frac{\sigma l}{{{\varepsilon }_{0}}B}\]

    B)  \[\frac{\sigma B}{{{\varepsilon }_{0}}l}\]

    C)  \[\frac{{{\varepsilon }_{0}}lB}{\sigma }\]

    D)  \[\frac{{{\varepsilon }_{0}}l}{\sigma B}\]

    Correct Answer: C

    Solution :

    Here, magnetic force = electrostatic force                  \[qvB=qE\] \[v=\frac{E}{B}\] \[=\frac{\sigma }{{{\varepsilon }_{0}}B}\] The time taken by electron to travel a  l distance  in that space \[t=\frac{l}{v}=\frac{l}{\frac{\sigma }{{{\varepsilon }_{0}}B}}\] \[=\frac{{{\varepsilon }_{0}}lB}{\sigma }\]


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