  In this work, a new approach is presented with the aim of showing a simple
way of unifying the classical formulas for the forces of the Coulomb's law of
electrostatic interaction ($F_C$) and the Newton's law of universal gravitation
$(F_G)$. In this approach, these two forces are of the same nature and are
ascribed to the interaction between two membranes that oscillate according to
different curvature functions with the same spatial period $\xi\pi/k$ where
$\xi$ is a dimensionless parameter and $k$ a wave number. Both curvature
functions are solutions of the classical wave equation with wavelength given by
the de Broglie relation. This new formula still keeps itself as the inverse
square law, and it is like $F_C$ when the dimensionless parameter $\xi =274$
and like $F_G$ when $\xi = 1.14198$x$10^{45}$. It was found that the values of
the parameter $\xi$ quantize the formula from which $F_C$ and $F_G$ are
obtained as particular cases.
