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 coonnected in a system shown is in equilibrum. 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 $\sqrt{2mgA{ϵ}_0}$



Tension in the string is equal to $mg$. This tension is balanced by attractive force between the capacitors plate.

Balancing the forces, we have,
$mg=\text{(electrostatic pressure)}\times A$

$mg=\frac{{\sigma }^2}{2{ϵ}_0}A(\because P=\frac{F}{A})$

$\Rightarrow mg=\frac{Q^2}{2{ϵ}_{0}A}(\because \sigma =\frac{Q}{A})$

$\Rightarrow Q=\sqrt{2mg{ϵ}_{0}A}$