bluuebunny/crossref_metadata_2025 huggingface dataset:
The photodiode array camera: A new method for acquiring airtrack data
Authors: Butler Crispin O. , Bergeron David
Published: March 2005

A linear photodiode array mounted in a camera body provides an excellent means of acquiring position-time information for gliders moving on an airtrack. Based on the output of a 512 photodiode array, a computer calculates positions of two gliders simultaneously with a resolution of 10 μm and accuracy of 400 μm along the full length of a 2 m airtrack. Motions lasting up to 5 min can be acquired at rates of 50 positions per second. The resulting data can be interpreted with the aid of spreadsheets and graphing programs. Setup, calibration, and operation of the apparatus are simple enough that students can design and perform their own mechanics experiments.
Delta function terms arising from classical point-source fields
Authors: Bowen Jeffrey M.
Published: March 2005

In the context of classical vector and tensor fields, the problem of consistently using delta functions to represent point sources is addressed. Specifically, a general expression for the gradient of a common term arising in point-source tensor fields is presented. It is shown that the differential product rule fails for terms containing the delta function.
Electrostatic fields with straight flux lines
Authors: Urbantke H.
Published: March 2005

Electrostatic vacuum fields having straight flux lines—so that flux lines are possible orbits for charged test particles—are shown to be restricted to those cases which come to mind immediately: the fields of a point charge, an infinite straight charged wire, and the homogeneous fields. The length of the argument is surprising.
Iodine molecular constants from absorption and laser fluorescence
Authors: Lewis E. L. , Palmer C. W. P. , Cruickshank J. L.
Published: March 2005

Absorption and laser-induced fluorescence spectra of the iodine molecule are compared as sources of molecular constants. The comparative simplicity of the fluorescence spectrum and the increased precision provide a vivid and direct understanding of the iodine molecular ground state.
On the use of linear CCD image sensors in optics experiments
Authors: de Izarra C. , Vallee O.
Published: March 2005

The use of linear CCD (coupled charge devices) photodiode arrays is presented through a quantitative study of Fraunhofer diffraction. Other optics experiments easily realized when using CCD photodiode arrays, i.e., spectroscopy and a mirage effect investigation, are also suggested.
Algebraic method for the quantum theory of scattering
Authors: Arickx F. , Broeckhove J. , Van Leuven P. , Vasilevsky V. , Filippov G.
Published: March 2005

A new method for calculating parameters in the quantum theory of scattering is discussed. The method is based on an expansion of the continuum wave functions in a discrete oscillator basis. General aspects as well as some specific applications are considered.
Application of the variational principle to perturbation theory
Authors: Hushwater V.
Published: March 2005

In this note I discuss briefly a rather unusual example of the use of the variational principle, which perhaps is interesting for someone who studies or teaches quantum mechanics.
Third electromagnetic constant of an isotropic medium
Authors: Nieves José F. , Pal Palash B.
Published: March 2005

In addition to the dielectric and magnetic permeability constants, another constant is generally needed to describe the electrodynamic properties of a linear isotropic medium. We discuss why the need for the third constant arises and what sort of physical situations can give rise to a nonzero value for it. This additional constant, which we call the ‘‘activity constant’’ and denote by ζ, can explain optical activity and other phenomena from a purely macroscopic and phenomenological point of view.
The image of the physicist in modern drama (Part 2)
Authors: Brouwer W.
Published: March 2005

In an earlier paper, we reviewed a number of post-World War II plays which focused on the role scientists, and more particularly physicists, ought to play in modern society. In this article we continue this type of review, concentrating on the plays of Charles Morgan, Archibald MacLeish, Carl Zuckmayer, and Tom Stoppard, using Thomas Shadwell’s classic play The Virtuoso to set the stage for the more modern plays. These plays portray, in the eyes of the playwrights, something of the image of science as a way of gaining knowledge about nature, but focus more strongly on the difficult choices faced by scientists in a world in which the social implications of scientific discoveries have become almost overwhelming.
On presenting wave–particle duality using a simulated detector for multiple slit diffraction
Authors: Vermillion Robert E.
Published: March 2005

Using a computer program and monitor to simulate a detector for multiple slit diffraction provides a realistic illustration of what is meant by wave–particle duality. An example program is described; results are presented with figures.
Dust off the neutron howitzer to teach nuclear physics!
Authors: DuBard James L. , Gambhir Alok
Published: March 2005

A wide variety of topics in nuclear physics can be taught in the undergraduate laboratory using just a few metallic samples for activation in a neutron howitzer. Rather than scorned for its low neutron flux, the neutron howitzer can be appreciated for its safety in the physics teaching laboratory and its usefulness in conjunction with high-resolution gamma spectroscopy.
Newton’s pail in Einstein’s lift
Authors: Fecko Marián
Published: March 2005

The classic Newton’s pail experiment performed in a freely falling lift is discussed.
Numerical integration of Newton’s equations including velocity- dependent forces
Authors: Gatland Ian R.
Published: March 2005

Numerical integration routines designed for introductory physics courses, such as the last-point approximation and the second Taylor approximation, are incompatible with velocity-dependent forces. A general purpose routine which handles resistive, Coriolis, and magnetic forces, as well as conservative forces, is obtained by combining the fundamental Euler method with Richardson extrapolation. Further, this Euler–Richardson method is almost as efficient as the last-point approximation and the second Taylor approximation for simple central force problems and is more efficient for difficult problems, such as Earth–Moon orbits.
Thermodynamics of Crawford’s energy equipartition journeys
Authors: Leff Harvey S.
Published: March 2005

Energy equipartition ‘‘journeys’’ proposed originally in the context of relativistic mechanics [F. S. Crawford, Am. J. Phys. 61, 317–326 (1993)] are examined thermodynamically. Equipartition is between ideal gases separated by an insulating piston. Each journey alternates slow adiabatic volume changes and zero-work adiabatic piston resettings effected by a benevolent Maxwell’s demon until temperature and pressure equalities exist. For the systems considered, reversible adiabatic thermodynamic processes are equivalent to slow mechanically adiabatic, constant-action processes. Because phase space mixing is assumed implicitly in thermodynamics, the piston jiggling step needed in Crawford’s mechanics-based treatment is unnecessary. Zero-work journeys maximize the gas system’s entropy change, and maximum work output journeys leave that entropy unchanged. Thermodynamics confirms Crawford’s result for the piston’s effective spring constant, and statistical mechanics enables rigorous justification of his interesting recursion relation for the moments of q=momentum×velocity.
Motion of a leaky pendulum
Authors: Mires Raymond W. , Peters Randall D.
Published: March 2005

The period of a physical pendulum whose mass and effective length vary with time has been studied both experimentally and theoretically. Results are given for both water and alcohol.
Numerical study of electron tunneling through heterostructures
Authors: Méndez B. , Domínguez-Adame F.
Published: March 2005

A numerical scheme based on the discretized form of the one-dimensional Schrödinger equation is presented. Using a transfer matrix method we recursively compute the transmission coefficient for electrons in arbitrary potentials. The computation time and storage are much reduced so that the code may be implemented by most programmable pocket calculators. The numerical method is used to study electron tunneling through single and double heterostructures, and the accuracy of the method is discussed.
How Galileo could have derived the special theory of relativity
Authors: Sen Achin
Published: March 2005

The kinematic results of the special theory of relativity are derived using only the first (Galilean) postulate and the results of one simple thought experiment. Our method is mathematically simple and, therefore, can be used in an algebra based introductory physics course. It is also pedagogically attractive because the relativistic results follow as a natural extension of the familiar Newtonian ones.
Orbital nonorthogonality effects in band structure calculations within the tight-binding scheme
Authors: Mirabella D. A. , Aldao C. M. , Deza R. R.
Published: March 2005

The consequences of orbital nonorthogonality on the structure of energy bands in the one-electron approximation are studied for an infinite one-dimensional monoatomic chain with nearest-neighbor interactions in the tight-binding scheme. Nearest-neighbor overlap introduces modifications into the band structure which affect the functional form of the band, in such a way that symmetry with respect to the corrected atomic level is lost. It is found that effective masses at the top of the band decrease while those at the bottom increase. It is shown explicitly how the nearest-neighbor nonorthogonality effects can be simulated by introducing more-distant-neighbor interactions while the orbital orthogonality requirement is maintained.
Discretization and truncation errors in a numerical solution of Laplace’s equation
Authors: MacDonald William M.
Published: March 2005

Numerical solutions to Laplace’s equation for an electrostatic potential can easily be found in undergraduate physics courses by approximating the Laplacian on a mesh and solving the resulting difference equations using a spreadsheet program or a simple program written in basic or pascal. The simplest numerical method uses iteration and accelerates the convergence by simultaneous overrelaxation (SOR). Truncating the iteration introduces an error in the solution to the difference equations, and this raises the question of how stringent to make the criterion for convergence. This paper considers the relative magnitude of the errors made in approximating the Laplacian (discretization error) and in truncating the iteration (truncation error). Numerical results are given for an electrostatic cavity problem previously investigated by several authors, and the numerical solutions are compared with an exact solution obtained by conformal mapping. It was found that when even a modest convergence criterion is used to truncate the iteration, the rms error inherent in discretization is more than an order of magnitude larger than the error in the solution of the difference equations. It was also found that the commonly used nearest-neighbor approximation to the Laplacian gives the most accurate numerical solutions.
‘‘Sagnac’’ effect: A century of Earth-rotated interferometers
Authors: Anderson R. , Bilger H. R. , Stedman G. E.
Published: March 2005

The earliest prediction of the Sagnac effect, and of the possibility of detecting the Earth’s rotation with an interferometer of square kilometer area, is by Lodge (1893, 1897). We illustrate the extraordinary range of theoretical motivations for the experimental study of the Sagnac effect, starting with previously unpublished correspondence between Lodge and Larmor, and ending with present (and planned) ring interferometer experiments whose sensitivity to the Earth’s rotation is of the order of parts per million (billion, respectively).
Uncertainty principle for joint measurement of noncommuting variables
Authors: Raymer M. G.
Published: March 2005

Does the Heisenberg uncertainty principle refer to errors of measurement, or to the spread of values of the physical variables intrinsic to a particle’s state, or to some combination of these? The most commonly quoted form of the uncertainty principle relates the spread of an ensemble of separate measurements of some variable to the analogous spread of its conjugate variable. In contrast, Heisenberg’s original argument for the uncertainty principle involved the perturbation to a particle’s state by a measurement of one variable, which affects one’s ability to predict the outcome of a subsequent measurement of the conjugate variable. The relation between these two views of the uncertainty principle is discussed in this paper. A familiar example is considered: an ensemble of identically prepared particles passing through a slit, and after further propagation being detected. From this arrangement it is possible to infer joint (although necessarily imprecise) information on both transverse position and conjugate momentum for each member of the ensemble. It is shown that in this case of joint measurement the product of standard deviations for the measurement outcomes is at least twice as large as the lower bound implied by the usual uncertainty principle. The discussion is meant to help clarify the different roles played in the various statements of the uncertainty principle by the initial state and by measurement error.
Further thoughts on Newton’s zero-order rainbow
Authors: Lock James A. , McCollum Timothy A.
Published: March 2005

A zero-order rainbow angle may be defined as the relative minimum angle of deviation of geometrical light rays transmitted without internal reflections through a transparent particle. If the incident rays are parallel and the particle is a sphere, such a minimum does not exist. But if the incident rays are not parallel or if the particle has an elliptical rather than circular cross section, an angle of minimum deviation, hence a zero-order rainbow, can occur. For a spherical water droplet, the zero-order rainbow will occur when a point source is placed less than a droplet radius away from its surface. If a column of water with an elliptical cross section is illuminated by a plane wave, a zero-order rainbow will occur if the length of the major axis of the cross section is more than twice the length of the minor axis.
Max Planck and the ‘‘black year’’ of German physics
Authors: Mulligan Joseph F.
Published: March 2005

1994 is the hundredth anniversary of what Max Planck described in 1935 as the ‘‘black year’’ of German physics. In the eight months between January 1st and September 8th 1894, Heinrich Hertz, August Kundt, and Hermann von Helmholtz died. This article reviews the lives of these three important physicists, their research contributions, and their unique positions in the German physics community. In conclusion, the relationships of these three physicists to Planck are discussed, and Planck’s evaluation of the impact of 1894 on physics in Germany is appraised from our perspective of one hundred years.
The circular disk parallel plate capacitor
Authors: Carlson G. T. , Illman B. L.
Published: March 2005

One of the more familiar systems in electrostatics is the parallel plate capacitor (PPC). While this system has received considerable attention in the close plate approximation, little is known about the exact solution for arbitrary plate separations. Although the solution was first given, in cylindrical coordinates by Sneddon, it was part of a more general treatise on mixed boundary value problems and appears to be unknown to much of the physics community. We present here a dedicated derivation of the solution to the boundary value problem for parallel disks, in cylindrical coordinates. The resulting expressions for potential and capacitance are in closed form, but depend on a function f(t) which is determined from an integral equation of the Fredholm type, known as Love’s equation. By adopting an orthogonal series approach to the solution of Love’s equation, we have calculated the capacitance for a number of plate separation to plate radius ratios. A quantitative measure of the close plate approximation is then presented by comparing these values to those one would obtain using the elementary capacitance equation ε0A/d.
Hellmann–Feynman theorem in a linear superposition of energy eigenstates
Authors: Balasubramanian S.
Published: March 2005

A generalization to the Hellmann–Feynman theorem is presented when the quantum mechanical state is a linear superposition of energy eigenstates. Some simple applications are discussed.
Remarkable shapes of a catenary under the effect of gravity and surface tension
Authors: Behroozi F. , Mohazzabi P. , McCrickard J. P.
Published: March 2005

The shape assumed by a hanging chain (the catenary) has been known for 300 years, since Leibnitz first published the correct equation of the catenary around 1690. We have investigated the shape of a hanging string when the area bounded by the string and the supporting rod is covered by a soap film. The competition between the surface tension and the normal component of the gravitational force per unit length determines the shape assumed by the hanging string. When the surface tension is dominant, the string assumes a convex shape similar to the Greek letter gamma. When gravity dominates, the shape is a distorted catenary. In the special case when the surface tension is exactly balanced by the normal component of the gravitational force per unit length, the string assumes a linear shape like the letter V. In this article the governing differential equations are derived for the general case and solved analytically to yield a pair of parametric equations for the x and y coordinates, describing the shape of the string. Numerical results based on these equations account very well for all the experimental features described above.
Once more the perturbed Kepler problem
Authors: Stahlhofen A. A.
Published: March 2005

A qualitative description of Kepler problems perturbed by external fields is presented using only the tools of elementary mechanics. All considerations can be based on a nonconserved Runge–Lenz vector. A transfer of these methods to related classical or quantum-mechanical problems is possible.
Spectral shifts in general relativity
Authors: Narlikar Jayant V.
Published: March 2005

A unified approach towards spectral shifts in general relativity brings the cosmological and gravitational redshifts within the same framework as the more familiar Doppler effect. This approach was first proposed by Synge [Relativity: The General Theory (North-Holland, Amsterdam 1960)] and is described here in a more simplified form.
Experiment on the motion of a dielectric in a parallel-plate capacitor
Authors: Meyer John J. , Behof Anthony F.
Published: March 2005

This article describes a relatively simple arrangement which can be used to study the motion of a dielectric slab in a parallel-plate capacitor. An aluminum cart fixed above a linear air track, together with the track itself, forms the capacitor, and a plastic rider serves as the dielectric. The electric force on the dielectric, partially withdrawn from the capacitor, is found to be proportional to the square of the voltage applied to the plates. Results for the motion of this dielectric are given for a fixed potential difference across the plates. A simple model including a frictional force is presented to describe this motion.
Simple method for demonstrating Fraunhofer diffraction
Authors: van der Gracht Joseph
Published: March 2005

A simple and inexpensive method is presented for displaying Fraunhofer diffraction in a classroom environment. Laser printers are used to create the input patterns and the diffraction patterns can be viewed without the use of a laser or lenses.
Implicit Lorentz transformations
Authors: Biritz Helmut
Published: March 2005

Lorentz transformations x′=Lx may be characterized by an implicit equation of the type x′−x=M(x′+x), where the matrix M is a simple linear combination of the generators of the Lorentz group. By means of such implicit equations we discuss the multiplication properties of Lorentz transformations, in particular products of boosts, using only elementary matrix calculus.
Exactly solvable noncentral potentials in two and three dimensions
Authors: Khare Avinash , Bhaduri Rajat K.
Published: March 2005

We show that the list of analytically solvable potentials in nonrelativistic quantum mechanics can be considerably enlarged. In particular, we show that those noncentral potentials for which the Schrödinger equation is separable are analytically solvable provided the separated problem for each of the coordinates belongs to the class of exactly solvable one dimensional problems. As an illustration, we discuss in detail two examples, one in two and the other in three dimensions. A list of analytically solvable noncentral potentials in spherical polar coordinates is also given. Extension of these ideas to other standard orthogonal coordinate systems as well as to higher dimensions is straightforward.
Students’ understanding of superposition of electric fields
Authors: Rainson S. , Tranströmer G. , Viennot L.
Published: March 2005

In this article an analysis of the difficulties experienced by students when applying the principle of superposition to electric fields is presented. A study of university level students in France and Sweden revealed the existence of difficulties arising out of two issues: (1) a causal interpretation of some relationships, (2) the student’s need for an effect, motion of some kind, to accept the existence of a field. The links between these obstacles and a lack of a unified view on electric phenomena are discussed from a pedagogical point of view.
Atoms as sources of multipole radiation
Authors: Huang Keh-Ning
Published: March 2005

Radiative transitions in atoms are formulated as multipole radiations from a localized charge-current distribution. The correspondence between the relativistic quantum mechanical and classical electrodynamic treatments is demonstrated explicitly. Definitions for multipole moments, line strengths, and oscillator strengths in relativistic quantum mechanics are also summarized.
Direct calculation of the electric and magnetic fields of an electric point charge moving with constant velocity
Authors: Jefimenko Oleg D.
Published: March 2005

Equations for the electric and magnetic fields of a point charge moving with constant velocity are derived from retarded integrals representing solutions of Maxwell’s equations for electric and magnetic fields of arbitrary time-dependent charge and current distributions. In contrast to conventional derivations, the derivations presented here are based exclusively on general electromagnetic field equations and do not make use of retarded potentials or relativistic equations. The derivations lead to some notable conclusions concerning the electric and magnetic fields of an arbitrary charge distribution moving with constant velocity.
Production and separation of C60 and C70 as an undergraduate experiment
Authors: Bradley D. S. , Massey J. L. , Mallik R. R. , Henriksen P. N.
Published: March 2005

Detailed instructions for producing and separating C60 and C70 are presented. The experiment involves elements of both physics and chemistry. After initial setup of the equipment, results are obtainable within a few hours. Additional experiments for observing physical properties of the fullerenes are suggested. A complete list of equipment is provided, with vendors and catalog numbers, for those wishing to duplicate the experiment.
Entropy and the second law: A pedagogical alternative
Authors: Baierlein Ralph
Published: March 2005

Thermodynamics in introductory physics typically begins with the ideas of temperature and heating and with the first law of thermodynamics. Then the more difficult parts come: entropy and the second law of thermodynamics. This second portion of the course can begin with a microscopic conception of entropy and a qualitative idea of how thermal systems evolve. The key concept is the ‘‘multiplicity of a macrostate:’’ the number of microstates associated with a macrostate. Starting from these notions—a point of departure and a concept—this paper develops the second law of thermodynamics, the relationship ΔS≥(energy input by heating)/T, and the Carnot efficiency. Offer the entire development both as a specific alternative to what appears in typical introductory texts and as a contribution to a continuing discussion of how to teach thermodynamics to various college audiences.
General relativity before special relativity: An unconventional overview of relativity theory
Authors: Rindler Wolfgang
Published: March 2005

It is suggested how Bernhard Riemann might have discovered General Relativity soon after 1854 and how today’s undergraduate students can be given a glimpse of this before, or independently of, their study of Special Relativity. At the same time, the whole field of relativity theory is briefly surveyed from the space–time point of view.
Motion of charges in crossed and equal E and B fields
Authors: Baylis W. E. , Bonenfant J. , Derbyshire J. , Huschilt J.
Published: March 2005

The classical motion of a charge e in an electromagnetic field F=E+iB (in units with c=1) is given by the component-free spinorial form of the Lorentz-force equation, namely, Λ̇=e/2m FΛ. Here m is the mass of the charge, and Λ represents the Lorentz transformation connecting the rest frame of the charge to the observer’s frame. The development is formulated in the geometric (Clifford) algebra of real three-dimensional space, the Pauli algebra, whose elements are all vectors in a complex four-dimensional space with the Minkowski spacetime metric. Explicit solutions are easy to write down for any constant and uniform E and B, and they take a particularly simple form in the case presented here of perpendicular fields of equal strength: F2=0.
Electromagnetic momentum density and the Poynting vector in static fields
Authors: Johnson Francis S. , Cragin Bruce L. , Hodges R. Richard
Published: March 2005

Many static configurations involving electrical currents and charges possess angular momentum in electromagnetic form; two examples are discussed here, an electric charge in the field of a magnetic dipole, and an electric charge in the vicinity of a long solenoid. These provide clear evidence of the physical significance of the circulating energy flux indicated by the Poynting vector, as the angular momentum of the circulating electromagnetic energy can be converted to mechanical angular momentum by turning off the magnetic field. Electromagnetic momentum is created whenever electric fields change in the presence of a magnetic field and whenever magnetic fields change in the presence of an electric field. When simple dielectrics are involved, the momentum density can be resolved into two components, a pure-field component ε0E×B and a component χeε0E×B associated with the polarization of the dielectric, the sum being εrε0E×B=D×B. It is argued that the latter component should be considered to be part of the electromagnetic momentum density, whose value then is D×B.
Magnetically imploded soft drink can
Authors: DeSilva A. W.
Published: March 2005

A demonstration apparatus is described suitable for use in a large lecture hall, in which the ‘‘pinch effect’’ applied to an empty aluminum soft drink can provides a dramatic and instructive example of induction and of the repulsion of oppositely directed current elements. The can is placed in a coil into which a short pulse of electrical current is driven from a charged capacitor. The current in the primary coil induces an oppositely directed current in the can wall, and the portion of the can under the coil is driven violently inward, pinching the can down to form a waist, or with a larger charge on the storage capacitor, separating it into two pieces.
Demonstrating different forms of the bent tuning curve with a mechanical oscillator
Authors: Weltner K. , Esperidiao A. S. C. , Andrade R. F. S. , Guedes G. P.
Published: March 2005

A mechanical rotating oscillator is used to demonstrate different bent tuning curves with basically the same system. A softening restoring force is realized by operating the oscillator as a gravitational pendulum. A hardening restoring force is realized by a spring acting on the oscillator. Tuning curves which are bent either to the right or to the left, as well as bistability and the jump effect, can be demonstrated. Furthermore, a doubly bent curve of amplitude versus frequency is shown to exist which gives rise to a doubly bent tuning curve and tristability. The experiments are a good introduction to unexpected phenomena related to nonlinear physics.
Consider a spherical battery...
Authors: Saslow W. M.
Published: March 2005

We introduce a simplified model of a ‘‘spherical battery’’ embedded within an infinite conducting medium, wherein the source of emf is taken to be a uniform vertical force per unit charge F, of nonelectrical nature. This model can be solved analytically for the surface charge distribution, the electric field, the electric current density, the magnetic field, the Poynting vector, and the angular momentum density. Through the net current and net power loss, a ‘‘lumped’’ resistance can be defined, and from the net current and the lumped resistance a lumped emf can be defined. This example explicitly illustrates that the surface charge on a battery causes it, at a distance, to behave like an electric dipole. It also provides an explicit example where the nonelectrical ‘‘field’’ of the battery acts only within the battery, whereas the electrostatic field of the surface charge acts both within and outside of the battery. A spherical inclusion within a material with otherwise uniform current flow is also analyzed to obtain the electric field, current density, and magnetic field. Additional geometries with current flow and surface charge, both with and without batteries, for which there exist analytic but sometimes complex solutions, are discussed. Following a discussion of voltaic cells, it is pointed out that in real voltaic cells the emf occurs at the electrode–electrolyte interface rather than throughout the volume. From that we propose a more realistic but less tractable model for a spherical battery, in which the emf acts only within two hemispherical shells.
Quantum mysteries explored
Authors: Jordan Thomas F.
Published: March 2005

A bare-bones skeleton of quantum mechanics is used to do the calculations underlying both Mermin’s example of a Bell inequality and his example of the Greenberger–Horne–Zeilinger discovery. An example of a recent discovery by Hardy also is discussed. It demonstrates the inconsistency between quantum mechanics and Einstein–Podolsky–Rosen assumptions in a way quite like that of Greenberger, Horne, and Zeilinger, without inequalities, but it requires only two particles with spin 1/2.
Radiation fields of a dipole in arbitrary motion
Authors: Heras José A.
Published: March 2005

We present a version of Jefimenko’s formulas for electric and magnetic fields in material media, and we demonstrate how this version of the formulas may be used for deriving the electric and magnetic fields produced by an arbitrarily moving dipole containing both electric and magnetic moments. Like the fields produced by a charge in arbitrary motion, the fields of an arbitrarily moving dipole can also be written in two forms: The Heaviside–Feynman form and the Liénard–Wiechert form. We derive here the first form and the radiation fields associated with the second form. These radiation fields are expressed by means of concise, symmetric, and illuminating formulas.
Electromagnetic field generated by a moving point charge: A fields-only approach
Authors: Donnelly Rod , Ziolkowski Richard W.
Published: March 2005

There are various methods for obtaining the electromagnetic field generated by an arbitrarily moving point charge in free space. If one decomposes the total electric field in terms of its transverse and longitudinal components, one must deal with the fact that the longitudinal component is propagated instantaneously. In this paper we deal with this in a novel manner. In the Fourier transform domain we solve for the transform of the transverse electric field in terms of expressions which involve the transforms of the current density and the longitudinal electric field; we thus view these expressions as ‘‘sources’’ of the transverse electric field. By inverse Fourier transforming we directly obtain the space–time transverse electric field, which is shown to contain a term which exactly cancels the instantaneous longitudinal electric field, so that the total electric field is propagated in a retarded fashion. Our approach does not make use of intermediate vector and scalar potentials, and thus dispenses with the need for gauge conditions.
Foucault pendulum ‘‘wall clock’’
Authors: Crane H. Richard
Published: March 2005

Details are given for the construction of a 70-cm-long Foucault pendulum to be mounted on the wall, and for a simple modification that will make it display local clock time. The possibility of having a Foucault pendulum of such short length is the result of finding new or improved ways of reducing four perturbing effects that become more severe as the length is decreased. They relate to: precession due to ellipticity in the motion, the drive system for maintaining the amplitude, the means of limiting the growth of ellipticity, and the method of gripping the suspending wire at the top. With those improvements, successful Foucault operation was attained in pendulums as short as 15 cm, support to center of bob. Following that severe test, the length for the ‘‘wall clock’’ was set at a conservative 70 cm. At that length it is highly reliable, and accurate to within 2% when timed for the full revolution. Uniformity in rate when comparing different intervals of azimuth is of course less. A simple method of making the pendulum read local time is described. Two clocks, one in the author’s office and one at home, have been in continuous operation for more than ten years.
Mach–Zehnder interferometer as an instructional tool
Authors: Nachman Paul
Published: March 2005

Students in our upper-division/graduate optics laboratory course assemble a Mach–Zehnder interferometer from simple components and use it to learn about interferometric principles and to visualize the phase-front geometries of light waves. Here we describe the experimental procedures, specify the equipment needed, and make suggestions for follow-up experiments.
Multislit diffraction patterns using a slit-grating combination
Authors: Mendelson Kenneth S. , Karioris Frank G.
Published: March 2005

A good quality transmission grating in conjunction with a fixed or adjustable slit can be used to demonstrate the significant features of the intensity distribution of a grating having a variable number of slits. With this technique, the study and demonstration can be extended to a large number of slits and can also show the transition from one integral number of slits to the next.
Cyclotron analog applied to the measurement of rolling friction
Authors: Edmonds Ian , Giannakis Nicholas , Henderson Chris
Published: March 2005

A simple and inexpensive analog of the cyclotron, ideal for demonstrating the concept of the cyclotron to large classes, is presented. A metal ball, constrained by a centrally directed spring force to follow a circular path over a plane surface, is accelerated by an alternating gravitational force provided manually. A simple method of recording the orbital radius of the ball in the analog provides a sensitive method of measuring the velocity dependent rolling friction force, F=a+bv. Values of a and b for rough and smooth wood surfaces are found and the mechanism by which the losses associated with rolling friction arise is discussed.
Simple soluble models of quantum damping applied to cavity quantum electrodynamics
Authors: Ligare Martin , Becker Stephen
Published: March 2005

We present two simple soluble quantum optical models in which an atomic system is coupled to a bath containing an infinite number of reservoir states. The total system is treated conservatively, but the atomic subsystem of interest exhibits decay. The first system consists of a single two-level atom coupled to an infinite number of modes of a one-dimensional cavity which are equally spaced in frequency. The coupling results in spontaneous emission by an excited atom into the modes of the cavity. The model also exhibits the subsequent re-excitation of the atom after the spontaneously emitted radiation is reflected from the ends of the cavity. The second is a single two-level atom coupled to a single mode of a damped optical cavity where the damping is provided by coupling to quantized oscillators in the walls of the cavity. The damped cavity alters the spontaneous emission rate from its free space value. The simplicity of both models makes them attractive as a method for introducing quantum mechanical damping phenomena.
Observing thermomigration of air bubbles in a fluid under gravity at an undergraduate research laboratory
Authors: Simard J.-F. , Houdayer A. , Boudreault R. , Bélanger S. , Laaouan A.
Published: March 2005

An educational experimental project in fluid mechanics for space science or physics honors undergraduates is presented. The motion of air bubbles in a viscous silicone oil in response to buoyancy and Marangoni convection is studied with an experimental setup adapted to the undergraduate laboratory. The Marangoni effect or thermocapillary convection occurs when a temperature gradient is present in the oil which generates a surface tension differential over the bubbles. Results of measured radii and temperature gradients necessary to balance the buoyancy and Marangoni forces, along with computed Marangoni velocities are in good agreement with previous terrestrial and space experiments.
The brightest beam in science: New directions in electron microscopy and interferometry
Authors: Silverman M. P. , Strange Wayne , Spence J. C. H.
Published: March 2005

An ultrasharp electron field-emission source, with emission region on the order of atomic size (i.e., fraction of a nanometer), produces a bright, strongly self-focused, highly coherent electron beam—indeed the brightest particle beam currently known to science. Employed in the configuration of a point-production microscope, this ‘‘nanotip’’ source facilitates low-energy electron imaging of fragile structures at atomic-scale resolution. When slightly out of focus, the microscope serves as perhaps the world’s simplest electron interferometer providing Fresnel diffraction patterns from which important information like effective source size, source brightness, and beam degeneracy can be determined. One remarkable feature of point sources is the perfect (i.e., aberration-free), lensless imaging of periodic structures at a denumerable set of focal planes with complete suppression of nonperiodic detail. The high degeneracy and coherent emission of an electron pointlike source can be exploited in new types of quantum interferometry involving correlated electrons.
Entropy and heat along reversible paths for fluids and magnets
Authors: Leff Harvey S.
Published: March 2005

An identity for the volume derivative of entropy along an arbitrary reversible path is derived and used to show that the heat to a fluid can attain both positive and negative values along certain negatively sloped paths in the pressure–volume plane. A temperature–entropy plot graphically illustrates this point. An analogous entropy identity for magnetic systems is derived and used together with a temperature–entropy plot to gain insights into paramagnetic behavior. In contrast with the ideal gas, a path for an ideal paramagnet can have both positive and negative heats only if it attains both positive and negative slopes in a magnetization vs magnetic field plot.
Control of the chaotic driven pendulum
Authors: Baker Gregory L.
Published: March 2005

A method of controlling chaos (due to Ott, Grebogi, and Yorke) is illustrated with a simulated chaotic pendulum. The method consists of stabilizing a previously unstable periodic orbit through a feedback mechanism that periodically adjusts the damping parameter of the pendulum. The presentation is pedagogical and describes the method in more detail than is typical of the research literature on controlling chaotic systems.
The two-dimensional harmonic oscillator at finite temperature and nonzero chemical potential
Authors: Haugerud H. , Ravndal F.
Published: March 2005

The two-dimensional harmonic oscillator has a conserved angular momentum. When it is in thermal equilibrium at finite temperature it can thus be ascribed a chemical potential. We find the dependence of the internal energy on the average angular momentum as a function of temperature. It is most instructive to perform the calculation in the path integral formalism for motion in imaginary time. This simple system is directly applicable to the description of a free gas of relativistic, charged bosons at finite temperature and charge density.
The Cartesian rank two representation of spherical tensors with an application to Raman scattering
Authors: van Kleef Eddy H.
Published: March 2005

The concept of Cartesian representations of lower rank spherical tensors is reviewed. To facilitate the introduction of the latter, basis vectors and tensors that transform according to the laws for spherical tensors are introduced, as well as a fast projection of a rank two Cartesian tensor onto its spherical components. From this the rotational invariants of the tensors are deduced. The method is applied to the problem of orientational averaging of the Raman polarizability tensor. General, complex, expressions for the depolarization ratio and the reversal ratio are derived. The entire treatment is carried out in a classical context.
Undergraduate laboratory: Principles of gel electrophoresis
Authors: Erramilli Shyamsunder , Österberg Fredrik , Vogelaar Bruce
Published: March 2005

An experiment to illustrate the principles of gel electrophoresis was devised for a freshman undergraduate laboratory for pre-medical students studying physics. Students investigate the dependence of the mobility of charged colored molecules under the influence of an electric field in an agarose gel. The results of the experiment were used to illustrate the importance of electric fields and viscous forces for macromolecular motion, and understand some of the physical principles behind electrophoresis.
On the fields of a torus and the role of the vector potential
Authors: Carron N. J.
Published: March 2005

A toroidal current distribution has nonvanishing exterior vector potential A, but zero exterior field B=∇×A=0. This property, together with the absence of fringing fields as in a cylindrical solenoid, makes it convenient for studies involving the vector potential in a field-free region, such as the Aharonov–Bohm effect, or the effect of A in a Josephson junction. We present an immediate general result of magnetostatics, and use it to easily compute A for a torus, to visualize the static vector potential for any current distribution, and to show how one can construct a current distribution to produce any desired A. When the torus current I varies in time, nonzero quasistatic fields E(t) and B(t) are produced (E∼ωI/r3 and B∼ω2I/r2). Radiation is also produced, with the radiation pattern of an electric dipole. The torus provides a counterexample to the common erroneous notion that if all multipole moments of a current distribution vanish then quasistatic fields and radiation must also vanish. We then formulate Maxwell’s equations in a way that obviates the role of gauge transformations. This ‘‘gauge irrelevant’’ form clarifies the relation of potentials to current sources, isolating the role of the transverse part of A. The general result from magnetostatics is extended to time-varying sources, revealing a seldom recognized symmetry of Maxwell’s equations, and showing how one can visualize A for an arbitrary time-dependent current source.
Do quantum jumps occur at well-defined moments of time?
Authors: Greenstein George , Zajonc Arthur G.
Published: March 2005

Shelved atom experiments appear to show clear evidence for quantum jumps. We use a gedanken interference experiment to demonstrate that a fundamental temporal ambiguity in the photon time-of-emission occurs in such transitions.
Rolling motion and crumpled surfaces
Authors: Mead Lawrence R. , Folse R. F. , Cole Anna
Published: March 2005

We discuss some aspects of a paper which appeared recently in this journal [F. F. Lima, V. M. Oliveira, and M. A. F. Gomes, Am. J. Phys. 61, 421–422, 1993] in which the fractional dimension of rolling crumpled surfaces is measured experimentally. We show that this experiment may not actually be measuring fractal dimension kinematically at all. In addition, we report a variation of their experiment using nonfractal grooved cylinders. The results indicate that large irregularities on the surface of ‘‘rolling’’ objects may lead to errors in the dynamic measurement of the dimension of crumpled surfaces.
Heisenberg’s lattice world: The 1930 theory sketch
Authors: Carazza Bruno , Kragh Helge
Published: March 2005

About 1930, physicists were increasingly frustrated about the infinities of quantum electrodynamics and the strange behavior of what were believed to be nuclear electrons. As a way out of the problems Heisenberg suggested that space be subdivided in cells of finite size, and indicated in a letter to Bohr the essence of his theory. In Heisenberg’s lattice world, the electron could metamorphose into a proton, and the atomic nucleus consisted of protons and heavy ‘‘photons.’’ We analyze Heisenberg’s fascinating (but unpublished) theory in its historical context, and suggest a detailed reconstruction of the lattice world idea contained in the letter to Bohr.
Answers to Shimony’s queries
Authors: Stapp Henry P.
Published: March 2005

I answer 8 questions by Professor Shimony about my book Mind, matter, and quantum mechanics within the framework of quantum mechanics and the Heisenberg formulation. (AIP)
Editorial: AJP’s 1994 Referees
Authors: Lemons Don S. , Romer Robert H.
Published: March 2005

Once again, on behalf of all of our authors and readers, we want to express our gratitude to AJP’s reviewers. During the calendar year 1994, the 592 reviewers listed below contributed one or more (in some cases, many more) referee reports on manuscripts submitted to this Journal. We all owe an enormous debt to their expertise and dedication. Don S. Lemons, Assistant Editor Robert H. Romer, Editor
A few remarks on the matching conditions at interfaces in electromagnetic theory
Authors: Hall Dennis G.
Published: March 2005

The matching conditions that describe the behavior of electromagnetic fields at an interface between two media are usually obtained from the integral form of Maxwell’s equations. There are pedagogical benefits to augmenting this approach with one that begins with the differential form of Maxwell’s equations and employs unit step functions and the Dirac delta function. With such an approach, it is possible to avoid the use of the rectangles and pillboxes introduced in the standard textbook derivation, make explicit in the matching conditions their dependence on the shape of nonplanar or irregular interfaces, and reveal the connection between the matching conditions and the permittivity-gradient (∇ε) terms that appear in the wave equations for the electric and magnetic fields.
Magnetism and mirror symmetry
Authors: Yao Carl
Published: March 2005

Symmetries play an important role in physics. In this article, we examine the relationship between magnetism and mirror symmetry. The reflection properties of the vector potential A(t) and the magnetic induction B(t) are obtained, and these properties are used to analyze some simple circuits.
Understanding the physics of meteoritic descent
Authors: Celnikier L. M.
Published: March 2005

The fall of a body through a planetary atmosphere is analyzed in a relatively simple, essentially analytic, manner, emphasis being placed on the physical processes involved.