Amperian Current Loop Research Articles

Radiation pressure and the linear momentum of the electromagnetic field in magnetic media

We examine the force of the electromagnetic radiation on linear, isotropic, homogeneous media specified in terms of their permittivity epsilon and permeability mu . A formula is proposed for the electromagnetic Lorentz force on the magnetization M, which is treated here as an Amperian current loop. Using the proposed formula, we demonstrate conservation of momentum in several cases that are amenable to rigorous analysis based on the classical Maxwell equations, the Lorentz law of force, and the constitutive relations. Our analysis yields precise expressions for the density of the electromagnetic and mechanical momenta inside the media that are specified by their (epsilon,mu ) parameters. An interesting consequence of this analysis is the identification of an "intrinsic" mechanical momentum density, (1/2)E xM/c(2), analogous to the electromagnetic (or Abraham) momentum density, (1/2)E xH/c(2). (Here E and H are the magnitudes of the electric and magnetic fields, respectively, and c is the speed of light in vacuum.) This intrinsic mechanical momentum, associated with the magnetization M in the presence of an electric field E, is apparently the same "hidden" momentum that was predicted by W. Shockley and R. P. James nearly four decades ago.

Is the magnetic moment of the neutron a dipole or an Amperian current loop?

In classical electrodynamics the two model representations of magnetic moments, viz. the dipole and the Amperian current loop models, give equivalent results. In contrast, for particles with overlapping wave functions, this equivalence breaks down. In the case of the neutron a heated theoretical debate in the 1930’s on the choice of the correct model has been experimentally settled in the 1950’s in favour of the current loop model. The question became of down-to-earth technical relevance in neutron spin echo spectroscopy.

Zeeman energy, interference and Neutron Spin Echo: A minimal theory

In some polarized neutron beam experiments, such as Neutron Spin Echo spectroscopy, it is essential to follow exactly the minute changes of the neutron kinetic energy due to interaction with the magnetic fields, e.g. in a spin flip process. It is emphasized that in the Amperian current loop model of microscopic magnetism, shown to be valid by the experiments, the Zeeman energy term can be treated as a bona fide potential energy. This allows us to describe both the spin and the spatial motion of the neutron by using simple notions of wave propagation across potential steps. In this picture Larmor precessions are represented as interference between two Stern-Gerlach states ↑ and ↓. The approach proves to be sufficient for the interpretation of all known polarized neutron beam phenomena, including crystal interferometry. It also leads to the surprising prediction that, as a pure quantum effect, under special circumstances the Larmor precession frequency can be different from its classical value.

La nouvelle vague in polarized neutron scattering

Abstract Polarized neutron research, like many other subjects in neutron scattering developed in the footsteps of Cliff Shull. The classical polarized neutron technique he pioneered was generalized around 1970 to vectorial beam polarizations and this opened up the way to a “nouvelle vague” of neutron scattering experiments. In this paper I will first reexamine the old controversy on the question whether the nature of the neutron magnetic moment is that of a microscopic dipole or of an Amperian current loop. The problem is not only of historical interest, but also of relevance to modern applicationas. This will be followed by a review of the fundamentals on spin coherence effects in neutron beams and scattering, which are the basis of vectorial beam polarization work. As an example of practical importance, paramagnetic scattering will be discussed. The paper concludes with some examples of applications of the vector polarization techniques, such as study of ferromagnetic domains by neutron beam depolarization and Neutron Spin Echo high resolution inelastic spectroscopy. The sample results presented demonstrate the new opportunities this novel approach opened up in neutron scattering research.

Forces acting on magnetic dipoles

An attempt is made to derive the forces acting on a point-like magnetic dipole by a structure-independent method. The force expression thus obtained is different from the Lorentz force applied to an Amperian current loop, as first pointed out by Shockley and James. An expression is obtained for the force acting on a neutral Dirac particle with an anomalous magnetic moment. The relativistic equations of motion are formulated, and the solutions in a homogeneous magnetic field are discussed. It is concluded that the dipoles are accelerated along the field.