where \(U_{e}\left(\alpha,V\right)=\ \frac{1}{2}C(\alpha)V^{2}\) is the electrostatic energy stored in the capacitor,\(U_{m}\left(\alpha\right)=Fx(\alpha)\) is the mechanical work done by the external load \(F\), and \(-qV\) is the electrical work supplied by the battery. We neglect the bending strain energy and gravitational energy of the dielectric film given its low thickness and relatively large external loads.
Equation 6 can be modified (using the relationship \(q=CV\))