Charged particle in a constant electric field: force on a parallel plate charged capacitor

Abstract

We analyze the problem about the motion of a classical charged particle with negligible radiation losses inside a parallel plate charged capacitor and determine mutual forces acting between the charge and insulating capacitor plates in the rest frame of the capacitor and in the rest frame of the charge, correspondingly. In the latter case, the force on the capacitor's plates additionally contains a component associated with the flow of energy of mechanical stresses in the plates. We show that the misbalance of forces of action and reaction in this system is compensated by the time variation of momentum of the inter-actional electromagnetic field created by the capacitor and charge, which ensures the conservation of total momentum. The results obtained are helpful for better understanding the interaction of point-like charge with a charged body of finite size.