Q. 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
A) $1/d$
B) $1/d^{2}$
C) $d^{2}$
D) $d$
Explanation
(b) $C = \frac{\varepsilon_{0}A}{x}$
$\therefore\frac{dC}{dt} = \varepsilon_{0}A\frac{d}{dt}\left( \frac{1}{x} \right) = \frac{- \varepsilon_{0}A}{x^{2}}\left( \frac{dx}{dt} \right) = \frac{- \varepsilon_{0}A}{d^{2}}\left( \frac{dx}{dt} \right)$
$\Rightarrow \left| \frac{dC}{dt} \right| = \frac{\varepsilon_{0}A}{d^{2}}v\ i.e.\left| \frac{dC}{dt} \right| \propto \frac{1}{d^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.