Scattering and Gradient Forces from the Electromagnetic Stress Tensor Acting on a Dielectric Sphere

The derivation of the scattering force and the gradient force on a spherical particle due to an electromagnetic wave often invokes the Clausius-Mossotti factor, based on an ad hoc physical model. In this article, we derive the expressions including the Clausius-Mossotti factor directly from the fundamental equations of classical electromagnetism. Starting from an analytic expression for the force on a spherical particle in a vacuum using the Maxwell stress tensor, as well as the Mie solution for the response of dielectric particles to an electromagnetic plane wave, we derive the scattering and gradient forces. In both cases, the Clausius-Mossotti factor arises rigorously from the derivation without any physical argumentation. The limits agree with expressions in the literature.