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May 1986

Volume 54, Issue 5, pp. 393-479

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Good physics, bad history

Victor Weisskopf

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 393

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Abstract Unavailable
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01.65.+g History of science

Charge momentum?

Gerald A. Kitzmann

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 393

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Abstract Unavailable
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06.20.Jr Determination of fundamental constants

Reduced mass and the Bohr radius

T. R. Sandin

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 393

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Abstract Unavailable
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03.65.Ge Solutions of wave equations: bound states

Tenure, salary, grants et al.

Ronald D. Edge

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 394

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01.40.-d Education
01.75.+m Science and society
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Editorial: ‘‘...to see it as it is...to know it as it isn’t...’’

John S. Rigden

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 397

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Abstract Unavailable
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01.70.+w Philosophy of science
03.65.Ta Foundations of quantum mechanics; measurement theory
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Sustained availability: A management program for nonrenewable resources

Albert A. Bartlett

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 398 | Cited 4 times

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The continued extraction from the earth of nonrenewable mineral and fuel resources is a cause for concern, particularly where the rates of extraction are growing. If the rate of extraction declines a fixed fraction per unit time, the rate of extraction will approach zero, but the integrated total of the extracted resource between t=0 and t=∞ will remain finite. If we choose a rate of decline of the rate of extraction of the resource such that the integrated total of all future extraction equals the present size of the remaining resource then we have a program which will allow the resource to be available in declining amounts for use forever. This program is called Sustained Availability (SA) and it is somewhat analogous to the program of ‘‘sustained yield’’ in the management of renewable resources such as agriculture. The mathematics of this program, the opportunities it presents, and its consequences are examined in detail.
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89.30.-g Fossil fuels and nuclear power

Simple electrostatic model of the structural phase transition

Alexander A. Berezin

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 403 | Cited 2 times

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A purely classical system of four equal point charges q which are free to move over the surface of a sphere is considered. In the equilibrium configuration all charges are located at the vertices of the regular tetrahedron inscribed into the sphere. If a weak uniform electric field E is directed along the z axis, one charge q will move to the position (0,0,R), while three others will form an equilateral inscribed triangle with the plane perpendicular to the field. An increase of the field will distort the tetrahedron [three charges uniformly shift towards the charge at (0,0,R)], keeping the field (z axis) as a C3‐symmetry axis. However, when E reaches the ‘‘critical’’ value E0=0.732q/R2, the system abruptly changes its symmetry: For E>E0 the equilibrium (least energy) configuration corresponds to all four charges located symmetrically at the corners of the inscribed square whose plane is perpendicular to E. Consequently, the field will now form a C4‐symmetry axis. This jumpwise C3→C4 symmetry change provides a simple classical model for the structural phase transitions when the spontaneous discontinuity arises during a continuous change of one of the intensive variables (in this model the electric field E). Several related open problems which may appear attractive for the modeling on personal computers are also outlined.
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41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems
41.60.-m Radiation by moving charges
61.50.Ks Crystallographic aspects of phase transformations; pressure effects

Velocities, refraction, and particle aspects of water waves

J. Ernest Breeding, Jr.

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 406

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Examples are presented which show that water waves behave in some ways like ‘‘fictitious particles.’’ The velocities and refraction equations are developed for a wave packet composed of nonparallel wave components. The relationships between Fermat’s principle, the Euler–Lagrange equation for rays, the ray curvature expression, Snell’s law, and Hamilton’s equations are discussed. The energy transmission rate of a hydron (water wave packet) is used to derive the shoaling and refraction coefficients. The total reflection of water waves is examined. The results for a hydron are compared with those of monochromatic waves.
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47.35.-i Hydrodynamic waves

Microcomputers as digital electronics

C. D. Spencer and P. F. Seligmann

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 411

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An instructional unit in which students build a microcomputer out of individual integrated circuits has been developed. It introduces the basic operations and design principles of computers, demonstrates the sequential cycles through which computers interface with external circuits, and provides, through machine code, insight into software at the most fundamental level. The computer consists of a Z‐80 microprocessor plus memory, I/O, load/test, and applications circuits. A special breadboard system is used to facilitate construction and testing.
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01.50.Qb Laboratory course design, organization, and evaluation
07.05.Bx Computer systems: hardware, operating systems, computer languages, and utilities
89.20.Ff Computer science and technology
85.40.-e Microelectronics: LSI, VLSI, ULSI; integrated circuit fabrication technology

Extending special relativity via the perplex numbers

Paul Fjelstad

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 416 | Cited 6 times

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In analogy to the complex numbers z=x+iy, where the ‘‘imaginary’’ i is such that i2=−1, a system of perplex numbers z=x+hy is introduced, where the ‘‘hallucinatory’’ h is such that ‖h‖=−1. This system, invented by four freshmen at St. Olaf College, appears to have relevance in physics. In particular, it provides a natural way to extend the usual formalism of special relativity to the case ‖v‖>c. This is done by means of a velocity parameter ϕ, such that v=c tanh ϕ, where tanh is an extension of the ordinary hyperbolic tangent function. The fact that this extension has two different angles ϕ for each velocity v accounts for the different approaches in the literature to superluminal phenomena.
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02.10.De Algebraic structures and number theory
03.30.+p Special relativity

Faraday’s law—Quantitative experiments

R. C. Nicklin

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 422 | Cited 7 times

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A cylindrical bar magnet is dropped through a coil which encircles a glass tube. A Commodore 64 computer equipped with an analog to digital converter digitizes and stores the resulting voltage pulse. The magnet velocity and the number of turns on the coil are varied and simple measurements on the voltage pulse give quantitative tests of Faraday’s law. Integration produces the total flux through the coil. Flux integral calculations which treat the magnet either as a dipole or as a uniformly magnetized cylinder lead to equations for the voltage pulses which give a good fit to the experimental data obtained with a set of variable area coils. Either model is good for radial distances >40% the magnet length. Other results include determination of dipole separation and pole strength and surface current density. A versatile program for data acquisition and inspection is described. Suggestions are made for demonstrations and laboratory work for students in introductory noncalculus and calculus based courses and for advanced experimental work for majors.
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01.50.Pa Laboratory experiments and apparatus
01.50.ht Instructional computer use
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

An experiment with two air tracks

K. Mita, W. Shirley, and C. R. Chang

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 428

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The analysis of a mechanical system with two air tracks is presented. The theoretical results are compared with the experimental data.
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01.50.Pa Laboratory experiments and apparatus
45.05.+x General theory of classical mechanics of discrete systems

Derivation of the mirror equation

John W. W. Burrows

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 432

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The mirror equation, giving the relationship between the object distance, the tangential image distance, the radius of curvature of a concave mirror, and the angle of incidence, is derived in a way which is different from that appearing in the literature. The derivation given here is for an ideally shaped mirror and involves no approximations. This new approach shows the equation to be more generally applicable than might otherwise be expected.
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42.15.Dp Wave fronts and ray tracing
74.20.-z Theories and models of superconducting state
42.15.Eq Optical system design
42.79.Bh Lenses, prisms and mirrors

Production and use of a light beam with an intensity proportional to the distance from the source

P. Langlois, A. Boivin, and R. A. Lessard

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 435

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A laser beam arriving at normal incidence on a sharp edge produces a diffraction edge wave which appears on an observation screen as a bright line perpendicular to the edge. Provided some conditions are satisfied, it is shown that the intensity of this edge wave is proportional, within a finite range, to the distance from the diffracting edge to the screen. A brief history of the edge wave theory, which was first proposed by Thomas Young in 1802 to explain diffraction phenomena, is presented. Experimental results using this interesting proportionality between the diffraction edge wave intensity and distance are shown. These results concern the monitoring of a glider’s position on an air track under various conditions.
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06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)
42.25.Gy Edge and boundary effects; reflection and refraction
42.25.Fx Diffraction and scattering
42.79.Qx Range finders, remote sensing devices; laser Doppler velocimeters, SAR, and LIDAR

On an apparent paradox in the motion of a smoothly constrained rod

Victor Namias

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 440

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The motion in a vertical plane of a straight rod constrained to move between two frictionless concentric circles is investigated. An apparent paradox arises because the reaction forces at the contact points are purely radial, and together with the rod’s weight, which acts at the center of mass, are uncapable of supplying the torque about the center of mass necessary for the rod’s rotation. A tentative explanation has been given by Carroll [Am. J. Phys. 52, 1010 (1984)], where a mysterious tangential contact force arising from an infinite radial contact force is invoked. We disagree with these conclusions. In postulating that the motion takes place according to certain prescribed geometrical constraints, one must always make certain that the laws of physics are respected, and the model must be chosen accordingly. A simple model consisting of an H‐shaped frame with four contact points is used to determine the nature of the contact forces and the origin of the torque. As the link between the two half‐rods of the H frame is reduced, a single rod is obtained which can be thought of as the limit of a sector whose angular width is made vanishingly small. The dilemma is resolved by showing that a singular angular density of contact force distribution prevails, but that the contact force itself is finite.
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45.05.+x General theory of classical mechanics of discrete systems

A simple solution of the two‐dimensional relativistic Kepler problem

Stanley A. Bruce

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 446 | Cited 1 time

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A two‐dimensional electron is described by an appropriate spin 1/2 bi‐dimensional Dirac equation. The special case of a hydrogenic atom in two dimensions is solved in order to obtain its energy spectrum and the total spread of its fine structure levels.
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03.65.Pm Relativistic wave equations
11.10.St Bound and unstable states; Bethe-Salpeter equations

The dielectrophoresis force

L. Benguigui and I. J. Lin

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 447 | Cited 6 times

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We present a simple and physically transparent calculation of the dielectrophoresis force, i.e., a force acting on neutral bodies in nonuniform electric fields in the cases of dc and ac fields.
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41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

Optical display of the ambiguity function and the diffraction pattern of a screw—An analogy

J. Sethuraman

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 450

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The Fraunhofer diffraction pattern of a screw is interpreted as an optical display of essential features of the ambiguity function of a chirp signal. Since no special preparation and optical processing are needed for diffraction, the optical display is very simple to demonstrate and impressive to visualize.
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42.25.Fx Diffraction and scattering
42.30.Sy Pattern recognition

Integral approach to scattering by a surface impurity

Douglas Lessie

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 452

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The integral approach to quantum mechanical scattering is exhibited heuristically in a one‐dimensional context and applied to the multiple scattering problem of conduction electron scattering by a surface impurity, where the impurity is modeled as a complex delta‐function potential. It is shown to provide a much more physically insightful solution than direct solution to the Schrödinger equation. The total reflection amplitude is revealed, and its behavior physically interpreted, as a multiple scattering series of impurity and barrier amplitudes coupled by appropriate phase shifts as the electron wave propagates back and forth between the impurity and surface barrier.
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03.65.Nk Scattering theory
72.10.Fk Scattering by point defects, dislocations, surfaces, and other imperfections (including Kondo effect)

Mechanical analog of optical retarders

H. M. Lai, Lai‐Yung Leung, Kwok‐Leung Lee, and K. P. Chik

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 455

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An anisotropic system, which is composed of only springs and metal balls, is shown to be similar to an optical retarder. A mechanical analog of a half‐wave plate is thus constructed and its performance is found in qualitative agreement with the theory. Such a system may serve as a useful demonstration in teaching wave propagation in anisotropic media.
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01.50.My Demonstration experiments and apparatus
07.10.-h Mechanical instruments and equipment
42.79.Ci Filters, zone plates, and polarizers

Scattering by two‐dimensional circular barrier, hard circle, and delta function ring potentials

I. Richard Lapidus

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 459 | Cited 9 times

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Scattering lengths are obtained for the scattering of particles from two‐dimensional circular barrier, hard circle, and delta function ring potentials using classical mechanics and quantum mechanics. These results will be of interest in a quantum mechanics course as a supplement to the discussion of three‐dimensional scattering.
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03.65.Nk Scattering theory
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The relativistic one‐dimensional square potential

G. Gumbs and D. Kiang

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 462 | Cited 3 times

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Abstract Unavailable
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03.65.Ge Solutions of wave equations: bound states

Real‐time microcomputer frequency analyzer

R. H. Good

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 463

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Abstract Unavailable
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01.50.My Demonstration experiments and apparatus
01.50.ht Instructional computer use
07.05.Hd Data acquisition: hardware and software
07.05.Kf Data analysis: algorithms and implementation; data management
07.05.Rm Data presentation and visualization: algorithms and implementation
07.05.Bx Computer systems: hardware, operating systems, computer languages, and utilities

Numerical methods for error evaluation

A. Kinsella

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 464 | Cited 1 time

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Abstract Unavailable
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06.20.Dk Measurement and error theory

A new method to measure the R and n of a convex lens

Song Li‐er

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 466

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
42.15.Eq Optical system design
42.79.Bh Lenses, prisms and mirrors
42.87.-d Optical testing techniques
42.15.Dp Wave fronts and ray tracing

The first annual meeting of the AAPT

Melba Phillips

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 469

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Abstract Unavailable
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01.10.Hx Physics organizational activities
01.10.Fv Conferences, lectures, and institutes
01.65.+g History of science

A comparison of Kane’s equations of motion and the Gibbs–Appell equations of motion

Edward A. Desloge

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 470 | Cited 1 time

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Abstract Unavailable
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45.05.+x General theory of classical mechanics of discrete systems

Rebuttal to ‘‘A comparison of Kane’s equations of motion and the Gibbs–Appell equations of motion’’ [Am. J. Phys. 54, 470 (1986)]

T. R. Kane

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 472 | Cited 1 time

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Abstract Unavailable
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45.05.+x General theory of classical mechanics of discrete systems

Erratum: ‘‘Quantization of the Thomson atom’’ [Am. J. Phys. 52, 35 (1984)]

J. Sivardiere

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 472 | Cited 1 time

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Abstract Unavailable
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31.15.-p Calculations and mathematical techniques in atomic and molecular physics
99.10.Cd Errata

Erratum: ‘‘Science and superstition: Comets and the French public in the 18th century’’ [Am. J. Phys. 54, 16 (1986)]

Philip Stewart

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 472

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Abstract Unavailable
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01.75.+m Science and society
96.30.Cw Comets
99.10.Cd Errata
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A simple cloud chamber for television display

Haym Kruglak and Don Kangas

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 473

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Abstract Unavailable
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01.50.My Demonstration experiments and apparatus
07.07.Hj Display and recording equipment, oscilloscopes, TV cameras, etc.
29.40.Cs Gas-filled counters: ionization chambers, proportional, and avalanche counters

Mechanical equivalent of heat: Electrical method by vaporization of liquid nitrogen

T. E. Neil and P. D. Schulze

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 474

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
64.70.F- Liquid-vapor transitions
05.70.-a Thermodynamics
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Topology and Geometry for Physicists

Charles Nash, Author, Siddhartha Sen, Author, and John Stachel

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 476

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Abstract Unavailable
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01.30.Ee Monographs and collections
02.40.Pc General topology

The Young Einstein: The Advent of Relativity

Lewis Pyenson, Author and Clinton Van Siclen

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 476

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Abstract Unavailable
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01.30.Ee Monographs and collections
01.60.+q Biographies, tributes, personal notes, and obituaries

Statistical Physics and the Atomic Theory of Matter, from Boyle and Newton to Landau and Onsager

Stephen G. Brush, Author and Martin J. Klein

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 477

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Abstract Unavailable
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01.30.Ee Monographs and collections
01.65.+g History of science
05.70.Fh Phase transitions: general studies
51.10.+y Kinetic and transport theory of gases

Telescopes, Tides, and Tactics: A Galilean Dialogue about the Starry Messenger and Systems of the World

Stillman Drake, Author and Michael S. Mahoney

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 478

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Abstract Unavailable
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01.30.Ee Monographs and collections
01.65.+g History of science
95.30.Sf Relativity and gravitation

Concepts of Quantum Optics

P. L. Knight, Author, L. Allen, Author, and Neal B. Abraham

American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 479

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Abstract Unavailable
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01.30.Ee Monographs and collections
42.50.-p Quantum optics
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