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CET Karnataka Engineering CET - Karnataka Engineering 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 A uniform magnetic field B also exists in the space perpendicular to the direction of E. The electron moves perpendicular to both \[\overrightarrow{E}\] and \[\overrightarrow{B}\] without any change in direction. The time taken by the electron to travel a distance l in the space is

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

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

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

    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 distance \[l\] in that space                 \[t=\frac{l}{v}=\frac{l}{\frac{\sigma }{{{\varepsilon }_{0}}B}}\]                                 \[=\frac{{{\varepsilon }_{0}}lB}{\sigma }\]


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