Comparison of three methods for the evaluation of the electric force on a particle in electrophoresis

The electric force acting on a particle in electrophoresis is evaluated by three methods often used in the literature and the applicability of these methods under typical conditions is discussed. Using the electrophoresis of a rigid sphere at an arbitrary position in a spherical cavity, we show that, the choice of a method depends largely on the charged conditions on a surface and the symmetric nature of a system. If a method is inadequately chosen, not only the quantitative behavior of the mobility of a particle but also its qualitative behavior will be wrong predicted.