A parallel plate capacitor of plate area A, plate seperation d is charged potential difference V. The battery is then removed and a slab of dielectric constant k is inserted between plates of capacitor. If $Q,\in$ and $w$ denotes charge , electric field (after slab is inserted ) and work done on the system in process of inserting the slab, the incorrect relation is :

Question

$(A)\;Q= \frac{\in _0 AV}{d} \\ (B)\;E= \frac{V}{kd} \\ (C)\; w= \frac{\in_0 AV^2}{2 kd} \\ (D)\;w= \frac{\in _0 AV^2}{2d} (1-\frac{1}{k})$