We consider a charged colloidal sphere undergoing steady migration under an imposed electric field through an uncharged hydrogel, modeled as a Brinkman medium. The transport of ions is governed by the Nernst-Planck equation coupled with the Brinkman equation for fluid flow and Poisson equation for electric field. The motion deterring effects due to the induced electric field and electroosmosis in a gel medium are governed by the degree of the double layer polarization and electromigration of ions. These effects are correctly accounted in the present model. Based on the effective medium (EM) approach, we have estimated the mobility of the particle through the balance of hydrodynamical and electrical forces for a wide range of electrokinetic parameters such as, charge density of the particle, hydrogel permeability and ionic concentration (Debye layer thickness). A correct measure of the hydrodynamical drag and electrical force experienced by the particle in electrophoresis is made. We have validated our computed results for mobility by comparing with the available experimental and theoretical results. The role of electroosmosis on the hydrodynamics of the particle is analyzed by comparing the drag with the corresponding uncharged case. Our results suggest that the retardation effects are strong for moderate values of the Debye-Huckel parameter and grow as the permeability of the hydrogel is increased. (C) 2014 Elsevier Ltd. All rights reserved.