The present work deals with the electromigration interaction of non-Newtonian fluid in a rectangular micro capillary under the influence of an external electric field. In most of the chemical synthesis processes capillary electrophoresis plays a vital role in separation of chemical species from the mixture, where the concentration of sample ions is comparable to that of the background ions and the effect of electromigration becomes pronounced. A constant electric field is applied through the rectangular micro capillary to drive the non-Newtonian fluid with a combined force resulting from the electroosmosis and electrophoresis. The incompressible Navier-Stokes equation combined with volume density of electrical forces is considered for the flow transport incorporated with Nernst-Planck equation for ion transport. The analytical observation of electrical conductivity in a linear planar uniformly charged substrate is found to change locally near the sample peak and the electric field and migration velocity are concentration dependent. The analytical estimation of the velocity and potential are made with the implementation of suitable approximations considering the local-electric neutrality condition.The species calculation is arrived at from an area averaged nonlinear advection diffusion equation. It is observed that Taylor-Aries dispersion effect is dependent on the flow behavior index of the power law fluid similar to the case observed in Newtonian fluid as predicted by Ghosal and Chen [1].