Question

The plates $S$ and $T$ of an uncharged parallel plates 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 $\text{pC}$.

Answer 1

FBD of given system is shown in figure:

Force with which both plates S and T attracts, $F=\frac{q^2}{2A{\epsilon }_0}$
Since system is in equilibrium $T=mg$ and $F=T$

$\Rightarrow mg=\frac{q^2}{2A{\epsilon }_0}$

$\Rightarrow q=\sqrt{2mgA{\epsilon }_0}$

$\Rightarrow q=\sqrt{2\times {10}^{-7}\times 10\times 2\times {10}^{-6}\times 9\times {10}^{-12}}$

$\Rightarrow q=6\times {10}^{-12}\text{C}$

$\Rightarrow q=6\text{pC}$