In this paper we develop a modified Lagrangian for electrostatics based on the concept of voltage non-additivity, using recently-derived voltage boost transformation laws. Using a single dimensional physical space as a model, we solve the Euler-Lagrange equations for the electrostatic potential. It is shown that the modified electrostatic potential takes the form of a hyperbolic tangent function, where the function is approximately linear around the origin with horizontal asymptotes at the positive and negative Planck Voltages. Moreover, it is shown that the modified electrostatic Lagrangian automatically gives rise to classical gravitation as the leading correction term in the Taylor expansion of the solution. This provides a new interpretation of gravitation as a corrective term for electrostatics at very high voltages, wherein that term helps correct the potential in such a way that it never reaches the Planck Voltage. It is therefore a somewhat unique example of a unified field theory that does not assume the existence of extra dimensions. Future directions are discussed including possible implications for quantum gravity.