Plates S and T of an uncharged parallel plate capacitor are connected across a battery. battery is t

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1. Electric Charges and Fields

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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 = $A$]

A

$\sqrt {2mgA{ \in _0}} $

B

$\sqrt {\frac{{4mgA{ \in _0}}}{k}} $

C

$\sqrt {mgA{ \in _0}} $

D

$\sqrt {\frac{{2mgA{ \in _0}}}{k}} $

Solution

Force on metal plate $S$ due to electrostatic force by plate $T$ is $\frac{Q^{2}}{2 A \epsilon_{o}}$

Force exerted on plate $S$ by spring is $m g$

In equilibrium $\frac{Q^{2}}{2 A \epsilon_{o}}=m g$

or

$Q=\sqrt{2 m g A \epsilon_{o}}$

Standard 12

Physics

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