A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference Vo. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plate is

Question

Infinity Learn · Accepted Answer

Here $$C=$$ε$$0Ad$$ and $$Q=CV=$$ε$$0AV0d$$∴Energy stored, $$E1=Q22C=$$ε$$02A2V022d2CWhen$$ battery is disconnected, Q remains the same. As d increases to $$3$$ times, C decreases to $$3$$ times.∴ $$E2=3Q22C=3$$ε$$02A2V022d2CNow$$, Work done $$=$$ $$E2$$ $$-$$ $$E1$$∴ $$W=3$$ε$$02A2V022d2C$$−ε$$02A2V022d2C=$$ε$$02A2V02d2C$$            $$=$$ε$$02A2V02d2$$×ε$$0A/d=$$ε$$0AV02d$$

A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference V_o. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plate is

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