Question

The plates $\text{S}$ and $\text{T}$ of an uncharged parallel plates capacitor are connected across a battery. The battery is then disconnected and the charged plates are connected as shown in the figure. The sytem shown is in equilibrium. All the strings are massless. The magnitude of charge on one of the capacitor plates is [Area of plates $=A$]

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

Answer 1

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


The free body diagram of the given problem:

Under the equilibrium:

Force between the plates $=mg=T....\left(1\right)$

Let, the charge on the plates be $Q$, then the force on each plates due to the electric field between them is given by,

$F_Q=QE=Q\times \frac{Q}{2{\epsilon }_{0}A}=\frac{Q^2}{2{\epsilon }_{0}A}$

This will be equal to $T$,

So, using equation $\left(1\right)$,

$mg=\frac{Q^2}{2{\epsilon }_{0}A}$

$\Rightarrow Q=\sqrt{2mgA{\epsilon }_o}$

Hence, option (a) is correct answer.