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Question

# A parallel plates capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles, then

A
the charge on the capacitor increases
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B
the voltage across the plates increases
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C
the capacitance increases
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D
the electrostatic energy stored in the capacitor increases.
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Solution

## The correct option is D the electrostatic energy stored in the capacitor increases.Charge on plate is q Capacitance of parallel plate capacitor is C=ϵ0Ad we know that q=CV ⇒V=qC Potential energy stored in capacitor is U=q22C Given that distance between capacitors is increased to d′ Charge on plate remains q as charging battery is removed. The charge on the capacitor remains constant. New capacitance C′=ϵ0Ad′<C Capacitance decreases as the plates of capacitor are moved farther apart. The options (a) and (c) are incorrect. Potential across the plates V=qC′>qC Hence V increases. Option (b) is correct. Energy stored in the capacitor U=12q2C′>12q2C ∴U increases. Option (d) is correct.

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