Q. A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If $x$ is the separation between the plates, the time rate of change of electrostatic energy of capacitor is proportional to
A) $x^{- 2}$
B) $x$
C) $x^{- 1}$
D) $x^{2}$
Explanation
(a) $U = \frac{1}{2}CV^{2} = \frac{1}{2}\left( \frac{\varepsilon_{0}A}{x} \right)V^{2}$
$\therefore\frac{dU}{dt} = \frac{1}{2}\varepsilon_{0}AV^{2}\left( - \frac{1}{x^{2}}\frac{dx}{dt} \right) \Rightarrow \frac{dU}{dt} \propto x^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.