Wake potential and stopping power for a charged particle moving outside a nanosphere

The interaction of a charged particle with a nanosphere is studied based on the dielectric response theory. We obtain the analytical expressions of the induced potential and stopping power, as the charged particle moving outside the nanosphere with a constant velocity. From our results, since the spherical shape limitation, the well-known V-shaped wake effect tracing the particle cannot be observed clearly no matter at the nanosphere surface or in the bulk. Besides, we also find that the particle can even gain energy from the electron polarization as the particle moves to the nanosphere at relatively low velocity.