We delineate a multiscale and multiphysics electromechanical system modelling the response of dielectric elastomer and quantify its macroscopic behaviour. Our approach involves formulating a precise theoretical framework within the main laws of thermodynamics. In the initial stage, constitutive laws are derived through a generalized Coleman–Noll procedure. Subsequently, the constitutive laws are refined using a linear approximation of the response function and homogenization theory. This assumes rapidly oscillating space-charges as a source term in a moderately strong electric field. The approach involves an indirect method that approximates the quasi-static Maxwell’s equations in free space, combined with the periodic homogenization asymptotic procedure. Employing the periodic unfolding operator and the averaging operator facilitates the transition to the homogenization limit, revealing the pivotal role of correctors in bridging the gap between microscopic and macroscopic aspects by quantifying disparities between heterogeneous and homogenized solutions.