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

Answer 1

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

At equilibrium,
mg = kx = force between the plates.
$mg=\frac{q^2}{2{ϵ}_{0}A}$
$\Rightarrow q=\sqrt{2mgA{ϵ}_0}$