This study focuses on the static pull-in instability of electrostatically actuated nano-cantilevers subjected to the van der Waals (vdW) attraction. For this aim, the equivalent mass-spring model with equivalent mechanical properties is considered. The non-linear set of governing equations of equilibrium and stability are also derived and solved analytically using homotopy perturbation method (HPM). The solutions indicate that there exist a linear relationship between the normalized pull-in voltage and dimensionless properties of the system. Employing this linear relationship, pull-in voltage as well as the maximum allowable length of the beam, the so-called detachment length of the beam, are extracted explicitly through some closed-form solutions. The solutions are validated through direct comparison with available results in the literature and excellent agreements between them are observed.

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