Let B ⊂ R N be the unit ball. We study the structure of solutions to the semilinear biharmonic problem where p, λ > 0, which arises in the study of the deflection of charged plates in electrostatic actuators. We study in particular the structure of solutions for N = 2 or 3 and show the existence of mountain-pass solutions under suitable conditions on p. Our results contribute to completing the picture of solutions in previous works. Moreover, we also analyze the asymptotic behavior of the constructed mountain-pass solutions as λ → 0.