A theoretical model is proposed to analyze the electrophoresis of a charged microparticle in an electrolyte-filled microchannel. The Poisson-Nernst-Planck equations are coupled with the mass and momentum balances before solving them numerically with appropriate boundary conditions. The model includes the efficacies of moving-deforming-mesh and fluid-structure interaction to uncover the accurate picture of such motions. An analytical model has also been developed to compare with the numerical results. The simulations reveal that the electrical double layer (EDL) develops dynamically surrounding the particle when it initiates electrophoresis. Unsteady motion of the particle is observed during the development stage of the EDL before a steady electrophoretic migration is established. Even during the steady migration, an asymmetric EDL surrounding the particle is observed. The electrophoretic velocity obtained are found to be consistently lower than the existing models. The influences of formation of the asymmetric EDL, the fluid structure interaction, and particle-inertia are found to be some of the major reasons for the deviations. The particle size, fluid viscosity, applied field intensity, and surface potential are found to influence the speed of the particles significantly. The drag around the particle, the wall drag near the confinement, and the variation in the electrophoretic thrust, due to the variation in the size of the particle, are found to be some other influential parameters. Interestingly, the speed and direction of the electrophoretic motion of the "Janus" particles can be tuned with the variation in the chemical heterogeneities on the surface.