The electrophoretic mobility U of a spherical particle in a spherical cavity for the case of low electric field is estimated for an arbitrary thick electrical double layer. We show that if the particle is uncharged and the cavity negatively charged, the deviation in the mobility based on the linearized Poisson-Boltzmann equation, U-L, can be serious even at a low electrical potential. In this case, the variation of the absolute deviation, \U - U-L\ as a function of kappa a, kappa and a being, respectively, the reciprocal Debye length and particle radius, has a maximum. The kappa a at which the maximal absolute deviation occurs increases with lambda (particle size/cavity size), and the maximal absolute deviation decreases with lambda. The latter increases with the absolute surface potential of cavity. If the particle is positively charged and the cavity uncharged, U-L is sufficiently accurate if the electrical potential is low.