Newton &-vs Lorentz

Abstract

Is there a point of divergence between Classical Mechanics and Electromagnetism? This discrepancy is raised by many authors and arises between Newton's third law and the equation of Lorentz forces. Due to the transcendence of these expressions, their wide application in different situations is not a minor issue and should be given a consistent interpretation with both theories. The discrepancy mentioned is based in that: according to the calculations of classical field theory, a particle with an electric charge moving immersed in a magnetic field suffers an action that diverts its trajectory, making it describe a circular path, which can not be compensated through a contrary force in the body that generated the magnetic field. The force on this second body is predicted, by this theory, at ninety degrees from the first, thus contradicting the principle of action and reaction. This study shows why the Lorentz law does not contradict Newton's third law and gives a consistent explanation of how the equations of classical field theory should be applied so that the result is correct.