On the origin of magnetic dynamics

Abstract

An examination of the origin of the torque on a magnetic dipole suspended above a line charge, as viewed from different frames of reference, provides insight into the nature of the dynamics of the magnetic interaction. In addition, it illustrates the remarkable unity of relativistic electromagnetic theory and points toward an intriguing interplay between geometry and dynamics.

Torque on a Moving Electric/Magnetic Dipole

“…(17) with other known expressions for the torque on an electric/magnetic dipole [3,4,[6][7][8][9][10][11], we notice that the first and second terms in rhs of this equation keep the form of the known components of torque exerted on a resting dipole (compare with Eq. (1)).…”

“…[3,4,[6][7][8][9][10][11]). The latter fact determines the goal of the present paper: to derive explicitly an expression for torque experienced by a moving dipole in an external EM field, to determine the physical meaning of various torque components in the approximation of a small dipole and to clarify the limits on application of the obtained equation.…”

Relativistic causality and conservation of energy in classical electromagnetic theory

“…However, the transformation from one frame to another might be a difficult task, and, as in many other examples, [15][16][17] an analysis in a different Lorentz frame allows one to see new physical phenomena; in our case it provides yet another possibility of making an error leading to a paradox.…”

Comment on “Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation”

“…[8][9][10]. It is also worth to mention that similar apparent paradoxes regarding the torque on magnetic dipoles were discussed and solved many years ago [3,11,12].…”