A parallel plate capacitor of plate area A and plate separation d is charged to potential V and then the battery is disconnected . A slab of dielectric constant K is then inserted between the plates of the capacitors so as to fill the space between the plates . If Q, E and W denote respectively the magnitude of charge on Each plate, the electric field between the plates (after$$ the slab $$inserted) and work done on the system in question in the process of inserting the slab , then state incorrect from the following:

Question

A parallel plate capacitor of  plate area A and plate separation d is charged to potential V and then the battery is disconnected . A slab of dielectric constant K is then inserted between the plates of the capacitors so as to fill the space between the plates . If Q, E and W denote respectively the magnitude of charge on Each plate,  the electric field between the plates (after$$ the slab $$inserted) and work done on the system in question in the process of inserting the slab , then state incorrect from the following:

Infinity Learn · Accepted Answer

After inserting the dielectric slabNew capacitance  C'$$=K$$.$$C=K$$ε$$0AdNew$$ potential difference  V'$$=VKNew$$ charge  Q'$$=C$$'V'$$=$$ε$$0AVd$$   Charge remains same.New electric filed  E'$$=V$$'$$d=VKdWork$$ done $$(W)=$$ Final energy – initial $$energyW=12C$$'V'$$2$$−$$12CV2=12KCVK2$$−$$12CV2$$ $$=12CV21K$$−$$1=$$−$$12CV21$$−$$1K$$ $$=$$−ε$$0AV22d1$$−$$1K$$ ⇒$$W=$$ε$$0AV22d1$$−$$1K$$

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