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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 = $A$ ]:

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A

$2 m g A \in_{0}$

B

$\frac{4 m g A \in _{0}}{k}$

C

$m g A \in_{0}$

D

$\frac{2 m g A \in _{0}}{k}$

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Solution

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Correct option is A)

Force on metal plate S due to electrostatic force by plate T is $\frac{Q ^{2}}{2 A ϵ _{o}}$
Force exerted on plate S by spring is $m g$
In equilibrium $\frac{Q ^{2}}{2 A ϵ _{o}} = m g$
or
$Q = 2 m g A ϵ_{o}$

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