The Secret Life of the Dipole

We consider the positions and velocities of electrons and spinning nuclei and demonstrate that these particles harbour hidden momentum when located in an electromagnetic field. This hidden momentum is present in all atoms and molecules, however it is ultimately cancelled by the momentum of the electromagnetic field. We point out that an electron vortex in an electric field might harbour a comparatively large hidden momentum and recognise the phenomenon of 'hidden hidden momen...

The interaction of a magnetic dipole with a point charge leads to an apparent paradox when analyzed using the 3-vector formulation of the Lorentz force. Specifically, the dipole is subject to a torque in some frames and not in others. We show that when analyzed according to the covariant 4-vector formulation the paradox disappears. The torque that arises in certain frames is connected to the time-space components of the torque in the rest frame, giving rise to "hidden" moment...

It is demonstrated, owing to the nonlinearity of QED, that a static charge placed in a strong magnetic field\ $B$\ is a magnetic dipole (besides remaining an electric monopole, as well). Its magnetic moment grows linearly with $B$ as long as the latter remains smaller than the characteristic value of $1.2\cdot 10^{13}\unit{G}$ but tends to a constant as $B$ exceeds that value. The force acting on a densely charged object by the dipole magnetic field of a neutron star is estim...

We show that the magnetic dipole energy term appearing in the expansion of the magnetic potential energy of a localized current distribution has the form $ U= + \bf{m} \cdot \bf{B}$ which is wrong by a sign from the well known $ - \bf{m} \cdot \bf{B}$ expression. Implication of this result in relation to the electric dipole energy $ - \bf{p} \cdot \bf{E}$, and the force and torque on the magnetic dipole based on this energy expression is also discussed.

We present an approach to compute the electric and magnetic dipole moments of an electron by using polarization and magnetization parts of the Dirac current. We show that these dipole moment expressions obtained by our approach in this study are in agreement with the current experimental results in the literature. Also, we observe that a magnetic field plays an important role in the magnitude of the electrical dipole moment of the electron.

In a recent paper [arXiv:1205.0096], we questioned the validity of the Lorentz law of force in the presence of material media that contain electric and/or magnetic dipoles. A number of authors have criticized our methods and conclusions. This paper is an attempt at answering the critics and elaborating the relevant issues in some detail.

Recently there have been suggestions that the Lorentz force law is inconsistent with special relativity. This is difficult to understand, since Einstein invented relativity in order to reconcile electrodynamics with mechanics. Here we investigate the momentum of an electric charge and a magnetic dipole in the frame in which both are at rest, and in an infinitesimally boosted frame in which both have a common velocity. We show that for a dipole composed of a magnetic monopole-...

In a recent Letter [arXiv:1205.0096], Mansuripur considers a magnetic dipole positioned at a fixed location from a point charge. Performing a Lorentz transformation to a laboratory frame where the charge distribution moves he finds that `a net torque acts on the dipole pair'. He then argues that `this torque in the (lab) frame in the absence of a corresponding torque in the (rest) frame is sufficient proof of the inadequacy of the Lorentz (force) law'. In this comment we de...

It is well known that a magnetic monopole-electric charge system carries an angular momentum in its electromagnetic fields. Here we show that in the Dirac string formulation of magnetic charge the monopole-electric charge system also carries a momentum in its electromagnetic fields. This overlooked field momentum arises from the Coulomb electric field of the electric charge and the solenoidal magnetic field of the Dirac string. This implies that the monopole-charge system mus...

Using realistic classical models of microscopic electric-charge electric dipoles and electric-current (Amperian) magnetic dipoles, it is proven that the Einstein-Laub macroscopic electromagnetic force on a macroscopic-continuum volume of these classical dipoles equals the sum of the microscopic electromagnetic forces on the discrete classical dipoles in that volume. The internal (hidden) momentum of the discrete Amperian magnetic dipoles is rigorously derived and properly inc...