A parallel-plate capacitor has plates of area A and separation d is charged to a potential difference V. The charging battery is then disconnected, and the plates are pulled apart until their separation is 2d. Derive expressions for the following quantities. (Use any variable or symbol stated above along with the following as necessary:ϵ0) (a) the new potential difference Vf, (b) the initial stored energy, (c) the final stored energy, (d) the work required to separate the plates.