When the capacitor is kept at a constant potential difference V, the work performed by the moment of electrostatic forces between the plates when the inner moveable plate is rotated by an angle dφ equals the increase in the potential energy of the system. This comes about because when charges are made, charges flow from the battery to keep the potential constant and the amount of the work done by these charges is twice in magnitude and opposite in sign to the change in the energy of the capacitor Thus
Now the capacitor can be thought of as made up two parts (with and without the dielectric) in parallel.
as the area of a sector of angle Differentiation then gives
The negative sign of Nz indicates that the moment of the force is acting clockwise (i.e. trying to suck in the dielectric).