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
Diffcult
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(b)$C = \frac{{{\varepsilon _0}A}}{x};$
$\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)$
$==>$ $\left| {\frac{{dC}}{{dt}}} \right| = \frac{{{\varepsilon _0}A}}{{{d^2}}}v$ i.e. $\left| {\frac{{dC}}{{dt}}} \right| \propto \frac{1}{{{d^2}}}$
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