In this paper, size dependent static behavior of micro and nano cantilevers actuated by a static electric field including deflection and pull-in instability, is analyzed implementing nonlocal theory. Euler-bernoulli assumptions are made to model the relation between deflection of the beam and bending moment. Differential form of the constitutive equation of nonlocal theory is used to find the revised equation for bending moment and substituting in the equilibrium equation of electrostatically actuated beams final nonlinear ordinary differential equation is arrived. Also the boundary conditions for solving the equation are revised and to analyze the size effect better governing equation is nondimetionalized. The one parameter Galerkin method is used to transform this equation to a nonlinear algebraic equation. Arrived algebraic equation is solved utilizing Newton-Raphson method. Size effect on the maximum deflection and deflection shape for various applied voltages is studied. Also effect of beam size on the static pull-in voltage is studied. Results indicate that the dimensionless beam deflection decreases as size decreases while the pull-in voltage increases and specially change of deflection and pull-in voltage is significant for nanobeams.

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