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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Critical Thinking

  • question_answer
    The plates of a parallel plate condenser are pulled apart with a velocity \[v\]. If at any instant their mutual distance of separation is \[d\], then the magnitude of the time of rate of change of capacity depends on \[d\] as follows                        [MP PET 1991]

    A)            \[\frac{1}{d}\]                     

    B)            \[\frac{1}{{{d}^{2}}}\]

    C)            \[{{d}^{2}}\]                         

    D)            \[d\]

    Correct Answer: B

    Solution :

               \[C=\frac{{{\varepsilon }_{0}}A}{x};\]  \ \[\frac{dC}{dt}={{\varepsilon }_{0}}A\frac{d}{dt}\left( \frac{1}{x} \right)\]\[=\frac{-{{\varepsilon }_{0}}A}{{{x}^{2}}}\left( \frac{dx}{dt} \right)=\frac{-{{\varepsilon }_{0}}A}{{{d}^{2}}}\left( \frac{dx}{dt} \right)\] Þ \[\left| \frac{dC}{dt} \right|=\frac{{{\varepsilon }_{0}}A}{{{d}^{2}}}v\] i.e. \[\left| \frac{dC}{dt} \right|\propto \frac{1}{{{d}^{2}}}\]


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