Question

The plates $S$ and $T$ of an uncharged parallel plate capacitor are connected across a battery. The battery is then disconnected and the charged plates are now connected in a system as shown in the figure. The system shown is in equilibrium. All the strings are insulating and massless. The magnitude of charge on one of the capacitor plates is [Area of plates = $A$]:

• A. $\sqrt{2mgA{\in }_0}$
• B. $\frac{\sqrt{4mgA{\in }_0}}{k}$
• C. $\sqrt{mgA{\in }_0}$
• D. $\frac{\sqrt{2mgA{\in }_0}}{k}$

Answer 1

The correct option is A $\sqrt{2mgA{\in }_0}$

Force on metal plate S due to electrostatic force by plate T is $\frac{Q^2}{2A{ϵ}_o}$
Force exerted on plate S by spring is $mg$
In equilibrium $\frac{Q^2}{2A{ϵ}_o}=mg$
or
$Q=\sqrt{2mgA{ϵ}_o}$