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  4. The insulated plates of a charged parallel plate capacitor (with small separation between the plates) are approaching each other due to electrostatic attraction. Assuming no other force to be operative and no radiation taking place, which of the following graphs approximately shows the variation with time (t) of the potential difference (V) between the plates ?

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Q. The insulated plates of a charged parallel plate capacitor (with small separation between the plates) are approaching each other due to electrostatic attraction. Assuming no other force to be operative and no radiation taking place, which of the following graphs approximately shows the variation with time $ (t)$ of the potential difference $(V)$ between the plates ?

WBJEEWBJEE 2018Electrostatic Potential and Capacitance

Solution:

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Force $=\frac{1}{2} \cdot \frac{\sigma}{\varepsilon_{0}} q$
$\therefore $ Relative acceleration of plates,
$a_{ rel }=\frac{2 F}{M}$
Potential difference, $V=E d\,\,\,\,\,\, \,\dots(i)$
where, $d=d_{0}-\frac{1}{2} a_{ rel } t^{2} $ $(\because$ plates are moving )
$\therefore \, V=E\left[d_{0}-\frac{1}{2} a_{ rel } t^{2}\right]$
This is a equation of a parabola with downward concavity.