The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Bénard-Marangoni convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed.