Table of contents

We give a derivation for the fields of a moving point charge from Jefimenko's equations without the usual cumbersome differentiation of retarded quantities.

The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector potentials in the two gauges is shown to satisfy a Poisson equation to which the inhomogeneous wave equation for this quantity can be reduced. The right-hand side of the Poisson equation involves an important but easily overlooked delta-function term that arises from a second-order partial derivative of the Coulomb potential of a point charge.

We consider a class of analytically solvable models of reaction–diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.

In celestial mechanics, qualitative and quantitative analyses of an orbit are usually based on the conserved angular momentum and total energy of the motion. It is shown that angular momentum and the eccentricity vector defined herein permit a much more concise derivation at the undergraduate level.

The alternative version of the Franck–Hertz experiment with mercury, in which a two-grid tube is used as a combination of electron gun, equipotential collision space and detection cell, was analysed recently in considerable detail. In particular, it was inferred that, at optimal pressure, the formation of peaks in the anode current at inelastic thresholds is mediated inside the detection cell by the large variation, a maximum at 0.4 eV, in the cross section for elastic scattering. This variation is due to a shape resonance in the electron-mercury system and is observable persuasively at the onset of anode current as a sharp peak followed by a clear minimum. In this paper, the passage of electrons through the second grid to the anode region is analysed in terms of kinetic theory. The discussion is based on a simplified expression for the electron current derivable from an approximate form of the Boltzmann transport equation that maintains the spatial density gradient but omits elastic energy losses. The estimated range of pressure underlying this kind of idealization is in good agreement with experiment. An explicit solution is obtained by constructing an analytic expression for the momentum transfer cross section of mercury using a recent theory of generalized Fano profiles for overlapping resonances. This solution is used in order to model successfully the formation of peaks at the threshold of anode current and at excitation potentials, and to explain the dependence of the observed profiles on the pressure and on the sign and magnitude of the potential across the detection cell.

Some connections between quantum mechanics and classical physics are explored. The Planck–Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the canonical commutation relations and the Maxwell–Lorentz equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as 'inverse correspondence' since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generalization to massive particles leads to the Klein–Gordon and Schrödinger equations. The difference between the quantum wavefunction of the photon and a classical electromagnetic wave is discussed in some detail.

A very simple procedure for studying the statistical properties of particle counting is shown. The output of a Geiger tube is connected to the parallel port of a PC which writes onto a file the time at which a particle was detected. From these data both the distribution probability P(n) of counting n particles in a given time and the probability distribution P(t) of time intervals can be easily measured. The device also allows the implementation of an artificial dead time. Effects of dead time on the above distributions are studied. Further exercises are suggested.

In this work, we describe an experimental setup in which an electric current is used to determine the angular velocity attained by a plate rotating around a shaft in response to a torque applied for a given period. Based on this information, we show how the moment of inertia of a plate can be determined using a procedure that differs considerably from the ones most commonly used, which generally involve time measurements. Some experimental results are also presented which allow one to determine parameters such as the exponents and constant of the conventional equation of a plate's moment of inertia.

The spatial filtering features of resistive grids have become important in microelectronics in the last two decades, in particular because of the current interest in the design of 'vision chips.' However, these features of the grids are unexpected for many who received a basic physics or electrical engineering education. The author's opinion is that the concept of spatial filtering is important in itself, and should be introduced and separately considered at an early educational stage. We thus discuss some simple examples, of both continuous and discrete systems in which spatial filtering may be observed, using only basic physics concepts.

Monodisperse two-dimensional foams are produced by trapping a layer of equal-volume bubbles between two glass surfaces. The application of an appropriately angled or curved surface imposes a specific variation of the bubble area with position in the foam. With this easily demonstrated technique the foam can be created in such a way as to reproduce conformal maps of the hexagonal honeycomb lattice to a good approximation.

An uncomplicated and instructive experiment is described for the determination of the refractive index of micro-objects suited to students at undergraduate level. This experiment is, furthermore, a useful method for refractive index determination in material research. Example results for mesoporous materials are presented for the first time which are interesting for research on porous guest/host materials. One of the materials has an extremely low refractive index.

By mapping the classical evolution equation of the form (which appears in various physical contexts) to a space curve, we obtain the classical analogues of the Schrödinger and Heisenberg pictures used in quantum mechanics. The analogy is further clarified by using the relationship between this equation and the evolution of a quantum two-level system.

With the traditional method of heating a house, the heat lost by the fire is equal to the heat received by the house. But a more ingenious scheme can take advantage of cold air outside the house, so that the house gets more heat than the fire loses, without any outside work being done. We analyse this scheme using finite-time thermodynamics, and show that this plan forces a significant slowdown in the rate at which heat is delivered to the house. If our devices are optimized to deliver heat to the house as quickly as possible, heat is still delivered relatively slowly, compared to the traditional method of heating a house, and the total heat delivered can at most be amplified by a factor of .

In 1898 Henri Poincaré referred to the speed of light as a probable limit speed but rashly asserted it would never as such be experimentally verifiable. Moving space vehicle measurements of the cosmic limit speed, however, without assuming it equals c, were described by Coleman (2003 Eur. J. Phys.24 301). A more elementary measurement is also possible, involving two mutually stationary vehicles with a third passing between them. A simple formula gives the limit speed in terms of signal speed c and three time intervals.

The correct relativistic relationship between linear momentum and velocity of a moving body of rest mass m is deduced economically. The argument is intended to be used in an introductory course on special relativity.