Volume 49, Issue 8, August 1981
 Letters To The Editor



Sports and physics
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Brief derivations of relativistic mass
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 Editorial


Editorial: Gerald Holton—physicist and humanist
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 Papers


Thermodynamics of blackbody radiation
View Description Hide DescriptionThe thermodynamics of homogeneous, isotropic, unpolarized electromagnetic radiation in a cavity with volume and temperature controllable as the independent variables is analyzed. Internal energy, pressure, chemical potential,enthalpy,Gibbs free energy,heat capacities, expansivity, and compressibility are all derived from the Helmholtz free energy. Topics treated are the third law, isothermal, adiabatic, and free expansion, throttling process, phase equilibrium, stability, and the Carnot cycle.

Surface properties of Kerr–Newman black holes
View Description Hide DescriptionThe magnitude of the proper acceleration of a stationary observer in the exterior Kerr–Newman geometry is used to determine an elementary property of the event horizon of a rotating charged black hole and to give a simple physical interpretation of its ’’surface gravity’’ as used in descriptions of the Hawking radiation. The global (nonlocal) nature of a black hole event horizon is also simply illustrated. The Kerr–Newman metric and the calculations based on it are presented in SI equations for the benefit of the many students and teachers in physics who rarely use any other system. To minimize the mathematical tools required we carry out the calculations in the well‐understood Boyer–Lindquist coordinates.

Physics of living in space: A new course
View Description Hide DescriptionA new course uses the prospect of living in space to motivate students to learn some basic physics and also to grapple with some larger questions about the differences between pure science and technology. Among the special features of this course are a set of exercises (two done with a computer graphics terminal), a treatment of dynamics that defines mass from the conservation of momentum rather than from Newton’s second law of motion, and a strong emphasis on weightlessness, rocket propulsion, orbital mechanics, and other aspects of physics relevant to how one might build an orbiting city in space and live there.

Hall effect in a plasma
View Description Hide DescriptionIn low‐density plasmas, such as the positive columns of glow discharges, the Hall effect is very large and easily observable. An elementary analysis, reproduced here, shows that the Hall voltage between opposite sides of such a column measures only half of that expected ideally in a conductor with the same carrier density. The reduction is caused by ambipolar diffusion of the carriers whose density distribution is distorted in the presence of a transverse magnetic field. A simple experimental arrangement is described in which the Hall voltage across a helium discharge column is determined as a function of magnetic field,discharge current, and gas pressure. Thus electron drift velocity and density are inferred. A simultaneous measurement of the resistivity then permits evaluation of the collision frequency. If the collision cross section for scattering of electrons by helium atoms is given, the electron temperature can be estimated. Variation of the parameters thus permits a study of the scaling laws for the glow discharge column. The experiment is found to be a very rewarding educational experience.

Illustrating gauge invariance in quantum mechanics through the free electron in a uniform time‐varying electric field
View Description Hide DescriptionThe nature of gauge transformations and gauge invariance in quantum mechanics about which there exists so much confusion in the literature is simply and pedagogically illuminated by first carefully investigating in various gauges the elementary problem of a free electron subject to a spatially uniform time‐dependent electric field, and by then utilizing the findings from this particular example to clarify some general misconceptions.

Euler angles, direction cosines, and angular momentum
View Description Hide DescriptionThe line of nodes e_{ n } for the Euler angles (φ, ϑ, χ) is o r t h o g o n a l to the plane of the two z axes e°_{ z } and e_{ z }. In the present paper we introduce two vectors, f°_{ z } and f_{ z }, i n the plane of the z axes such that the set (f°_{ z }, e_{ n }, f_{ z }) is b i o r t h o g o n a l to (e°_{ z }, e_{ n }, e_{ z }). These new vectors are so easily visualized that their components can be written down by inspection of the figure illustrating the definition of the Euler angles, and thus the direction cosine e°_{ r } ⋅ e_{ s } can be obtained simply. This derivation makes no use of matrices. The total angular momentum J for a system of particles, where the Euler angles are used as coordinates for overall rotation, is shown in a simple manner to be J = f°_{ z } p _{φ}+e_{ n } p _{ϑ}+f_{ z } p _{χ}, where (p _{φ}, p _{ϑ}, p _{χ}) are the momenta conjugate to (φ, ϑ, χ).

Fourier integral treatment yielding insight into the control of Gibb’s phenomenon
View Description Hide DescriptionThe phenonmenon of overshoot and the associated oscillation (Gibb’s phenomenon) that occur in the Fourier series approximation to a discontinuous function are investigated by considering the Fourier sum to be a special case of the Fourier integral transform. It is then shown that Gibb’s phenomenon can be reduced or eliminated by multiplying the Fourier transform of the desired function by an appropriate filter function; however, this also reduces the steep slopes representing the points of discontinuity. Two separate parameterized filter functions are presented that can be used in trade‐off studies to optimize the magnitude of the resulting oscillations and reduction in slope associated with the discontinuity.

Physical approach to the theory of constrained motion
View Description Hide DescriptionA mathematically elementary approach based entirely on Newton’s laws of motion and physical arguments to the problem of constrained motion subjected to general velocity‐dependent constraints is presented. Natures of constraint forces are extracted from constraint relations and, consequently, the equations of motion in Newton’s, Lagrange’s, and Appell’s form are obtained. D’Alembert’s principle is proved to be true for and only for holonomic constraints and constraints homogeneous in velocity dependence.

Quantum operators in generalized coordinates
View Description Hide DescriptionIt will be shown in this paper how to build quantum operators in generalized coordinates. A direct substitution of momentum operators in the classical expression suffices; the only condition being that this expression must be written in matrix form before the substitution. Specifically, we are then able to show that the two operators −ih/(∂/∂Q) and −ih/g ^{−1/2} (∂/∂Q)g ^{1/2}, and only these, are to be associated with generalized momenta.

The cat landing on its feet revisited or angular momentum conservation and torque‐free rotations of nonrigid mechanical systems
View Description Hide DescriptionThis paper explains the connection between rotation and the law of conservation of angular momentum and points out that macroscopic angular momentum need not be conserved if it can be transferred to spin. Exact equations giving the rotational motion induced by a given internal motion are derived and discussed.

The pendulum reborn: Time measurements in the teaching laboratory
View Description Hide DescriptionTo oppose the trend towards a formal, purely theoretical teaching of physics we present our first practical step at creating a lively laboratory practice at the first‐year university physics level in Brazil. Two pendula are used simultaneously as the system under study and the time measuring reference instrument. We describe how we integrate historical and cultural references within our laboratory practice.

Simple explanation of a well‐known collision experiment
View Description Hide DescriptionA well‐known collision experiment can be carried out with an arrangement of several identical elastic balls each suspended by two threads and in contact with one another: a certain number of the balls is displaced from its equilibrium position and then released, so as to collide with the remaining balls at rest. After the collision, the same number of balls moves away to the other side as had initially been displaced. It is shown that, contrary to common belief, the conservation laws of energy and momentum alone are not sufficient to explain this behavior. Indeed, a further condition must be satisfied by the system of balls; namely, it must be capable of dispersion‐free energy propagation.

Hydrogenlike atom in the potential V = r ^{2}(a+b cos^{2}θ): Second‐order perturbation theory
View Description Hide DescriptionWe report a calculation of the ground‐state energy of a hydrogenlike atom in an external potential given by V = r ^{2}(a+b cos^{2}ϑ), using the second‐order perturbation theory. The matrix elements, involving both the bound‐state and continuum‐state eigenfunctions, are explicitly evaluated. Implication of the result in the magnetic study of quasi‐two‐dimensional electron layers on a liquid‐helium surface is discussed.

Modern spectroscopy with a spectrometer by the optogalvanic effect
View Description Hide DescriptionAn experiment involving the optogalvanic effect suitable for the advanced physics laboratory is described. This experiment complements the usual basic experiment in atomic spectroscopy where spectra are recorded on photographic film with a spectrograph or with a monochromator and photomultiplier. The optogalvanic effect used the atoms being studied as the detector and a tunable dye laser as the source. Linewidths observed are those of the dye laser that are considerably smaller than those obtained with the usual laboratory monochromator. The student is introduced to the techniques of spectroscopy with pulsed dye lasers and to a spectrum for which L S coupling does not hold.

Singly refracting biaxial crystals: A curiosity in Maxwell’s electrodynamics
View Description Hide DescriptionThe little‐known fact that a biaxial crystal with a tensorpermittivity ε_{ i j } as well as a tensor permeability μ_{ i j } can have a single refracted extraordinary ray for arbitrary angles of incidence on arbitrary cuts of the crystal, provided it satisfies the material condition ε_{1}/μ_{1} = ε_{2}/μ_{2} = ε_{3}/μ_{3}, is demonstrated from first principles and the consequences are examined in some detail.

Flashlamp‐pumped dye laser as an undergraduate lab project
View Description Hide DescriptionState‐of‐the‐art dye lasers have been exhaustively discussed previously in the literature, however, few of these articles provide the essential bare details necessary to construct a simple working dye laser. This discussion presents an overview of the construction techniques of dye lasers suitable for student projects. Ease in construction, low cost, and tuneable output in the visible range make such lasers ideal for the junior‐level lab. Skills required to complete a dye laser include basic optics, electricity, and modern physics usually covered at the sophomore level.
