Boltzmann Transport Equation 1-2 has been modelled in close conjunction with Maxwell’s equation, investigations for 2D and 3D transport carriers have been proposed. Exact solution of Boltzmann Equation still remains the core field of research. We have worked towards evaluation of 2D and 3D solutions of BTE. Application of our work can be extended to study the electromagnetic wave transport in upper atmosphere i.e. ionosphere. We have given theoretical and numerical analysis of probability density function, collision integral under various initial and final conditions. Modelling of coupled Boltzmann Maxwell’s equation taking binary collision and multi species collision terms has been evaluated. Solutions of Electric Field (E) and Magnetic Field (B) under coupled conditions have been obtained. PDF convergences under the absence of electric field have been sketched, with an iterative approach and are shown in figure 1. Also 3D general algorithm for solution of BTE has been suggested.