The Faraday law of induction for an arbitrarily moving charge

Abstract

The Faraday law of electromagnetic induction for an arbitrarily moving charge is generalized and the expression for the force acting on the charge in an alternating magnetic field is obtained. It is shown that besides the Lorentz force perpendicular to the velocity of the particle, the Faraday force parallel to the particle velocity and proportional to it is acting on the charge, too. The equations of motion of the charged particle and the magnetic moment are obtained in the time-varying magnetic field. The problems of induction acceleration of charged particles (betatron) and induction heating of medium (plasma, plasma betatron) are considered.