A parallel plate capacitor has plates with area A & separation d. A battery charges the plates to a potential difference of V0. The battery is then disconnected & a di-electric slab of constant K & thickness d is introduced. Calculate the positive work done by the system (capacitor + slab) on the man who introduces the slab.
charges Q=CV=εoAdVo
work sone= Initial energy-Final energy
W=12ColdV2−Q22Cnew
=12(εoAd)V2o−AεoV2o2Kd
=εoAV2o2d[1−1K]