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$$ the slab is $$inserted) and work done on the system in question in the process of inserting the slab, then state incorrect relation from the following

Question

Infinity Learn · Accepted Answer

After inserting the dielectric slab New capacitance C'$$=K$$.$$C=K$$ε$$0AdNew$$ potential difference V'$$=VKNew$$ charge Q'$$=C$$'V'$$=$$ε$$0AVdNew$$ electric field E'$$=V$$'$$d=VKdWork$$ done (W) $$=$$ Final energy – Initial $$energyW=12C$$′V′$$2$$−$$12CV2=12(KC)VK2$$−$$12CV2=12CV21K$$−$$1=$$−$$12CV21$$−$$1K=$$−ε$$0AV22d1$$−$$1K$$ so |W|$$=$$ε$$0AV22d1$$−$$1K$$.

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