Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual…

The electrical circuit of the jumping ring experiment based on discharging a capacitor is optimized. The setup is scoop proof at 46 V and yet the ring jumps more than 9 m high. The setup is suitable for both lectures and student laboratory work in higher education. (Contains 1 table, 8 figures and 3 footnotes.)

The relation M = [mu] x B is presented in all elementary courses on electromagnetism, but it is usually given just for the simple case of a rectangular wire. We will present a completely general but elementary proof of this relation together with two more advanced proof methods. We will then provide some extensions: non-closed wires and…

The magneto-kinematic effect has been previously observed for the case of a rotating permanent magnet. Using this effect, this paper presents a novel method for calculation of the induced electromotive force (EMF) in a conductor for the case of rectilinear motion of a 25.4 mm diameter permanently magnetized sphere (magnetic dipole) past the…

I describe an elementary way of introducing electromagnetic field momentum. By considering a system of a long solenoid and line charge, the dependence of the field momentum on the electric and magnetic fields can be deduced. I obtain the electromagnetic angular momentum for a point charge and magnetic monopole pair partially through dimensional…

We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…

In this paper we demonstrate a surprising aspect of quantum mechanics that is accessible to an undergraduate student. We discuss probability backflow for an electron in a constant magnetic field. It is shown that even for a wavepacket composed entirely of states with negative angular momentum the effective angular momentum can take on positive…

We explore the consequences of a force density, [image omitted], studied by some authors, for the device designed by Lai (1980 "Am. J. Phys. 48" 658) to analyse which definition of electromagnetic momentum density, either Minkowski's or Abraham's, is consistent with mechanical torques that arise from the change in time of a magnetic field, which…

It is known that observers comoving with a uniformly accelerated point charge detect the electromagnetic field of a charge as a static electric field. We show that one can find a similar family of observers, which detect the field of a charge as a static electric field, in the general case of arbitrary point-charge motion. We find the velocities…

The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity…

Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic fields, the multipolar solutions do not share a standard derivation or notation. As a result, expressions…

Among the most startling experiences a student encounters is learning that, unlike electrons and other elementary particles, photons have no mass. Under certain circumstances, however, the light quantum behaves as if it did have a finite mass. Starting from Maxwell's equations, we discuss how this arises when light interacts with a charged plasma,…

The analysis of paraxial Gaussian beams features in most undergraduate courses in laser physics, advanced optics and photonics. These beams provide a simple model of the field generated in the resonant cavities of lasers, thus constituting a basic element for understanding laser theory. Usually, uniformly polarized beams are considered in the…

We consider the nonlinear oscillations of a simple spring-magnet system that oscillates in the magnetic field of an inductive coil excited with a dc current. Using the relations for the interaction of a coil and a magnet we obtain the motion equation of the system. The relative strengths of the terms of this equation can be adjusted easily by…

We show how the concept of the magnetic dipole moment can be introduced in the same way as the concept of the electric dipole moment in introductory courses on electromagnetism. Considering a localized steady current distribution, we make a Taylor expansion directly in the Biot-Savart law to obtain, explicitly, the dominant contribution of the…