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May 1988

Volume 56, Issue 5, pp. 391-478

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A wonderful, but puzzling educational experiment

Carl W. David

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 391

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01.40.G- Curricula and evaluation

A way to make instructional research a reality

Joel A. Michael

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 391

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01.40.G- Curricula and evaluation

Units in electrodynamics

Stephen Luzader

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 391

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06.20.F- Units and standards
03.50.De Classical electromagnetism, Maxwell equations
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Problem 1 for May

Edward M. Purcell

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 392

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89.20.Ff Computer science and technology

Problem 2 for May

Edward M. Purcell

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 392

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Abstract Unavailable
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92.10.Kp Sea-air energy exchange processes

Problem 3 for May

Edward M. Purcell

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 392

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97.60.Bw Supernovae
96.50.sf Interactions with terrestrial matter

Solution 1 for April

Edward M. Purcell

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 392

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45.05.+x General theory of classical mechanics of discrete systems
92.60.-e Properties and dynamics of the atmosphere; meteorology

Solution 2 for April

Edward M. Purcell

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 392

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75.30.Cr Saturation moments and magnetic susceptibilities
75.80.+q Magnetomechanical effects, magnetostriction

Solution 3 for April

Edward M. Purcell

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 392

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45.05.+x General theory of classical mechanics of discrete systems
87.17.-d Cell processes
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Editorial: Richard P. Feynman (1918–1988)

John S. Rigden

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 393

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01.60.+q Biographies, tributes, personal notes, and obituaries

Announcement: Robert H. Romer, New Editor of American Journal of Physics

John S. Rigden

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 394

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01.60.+q Biographies, tributes, personal notes, and obituaries
01.30.-y Physics literature and publications
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Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity

Michael S. Morris and Kip S. Thorne

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 395 | Cited 257 times

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Rapid interstellar travel by means of spacetime wormholes is described in a way that is useful for teaching elementary general relativity. The description touches base with Carl Sagan’s novel Contact, which, unlike most science fiction novels, treats such travel in a manner that accords with the best 1986 knowledge of the laws of physics. Many objections are given against the use of black holes or Schwarzschild wormholes for rapid interstellar travel. A new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings. It is essential in these solutions that the wormhole possess a throat at which there is no horizon; and this property, together with the Einstein field equations, places an extreme constraint on the material that generates the wormhole’s spacetime curvature: In the wormhole’s throat that material must possess a radial tension τ0 with the enormous magnitude τ0∼ (pressure at the center of the most massive of neutron stars)×(20 km)2/(circumference of throat)2. Moreover, this tension must exceed the material’s density of mass‐energy, ρ0c2. No known material has this τ0>ρ0c2 property, and such material would violate all the ‘‘energy conditions’’ that underlie some deeply cherished theorems in general relativity. However, it is not possible today to rule out firmly the existence of such material; and quantum field theory gives tantalizing hints that such material might, in fact, be possible.
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04.20.Jb Exact solutions
97.60.Lf Black holes

Henry Cavendish, Johann von Soldner, and the deflection of light

Clifford M. Will

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 413 | Cited 4 times

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The gravitational deflection of light based on Newtonian theory and the corpuscular model of light was calculated, but never published, around 1784 by Henry Cavendish, almost 20 years earlier than the first published calculation by Johann Georg von Soldner. The two results are slightly different because, while Cavendish treated a light ray emitted from infinity, von Soldner treated a light ray emitted from the surface of the gravitating body. At the first order of approximation, they agree with each other; both are one‐half the value predicted by general relativity and confirmed by experiment.
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01.65.+g History of science
04.90.+e Other topics in general relativity and gravitation (restricted to new topics in section 04)

The anthropic principle II

Joe Rosen

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 415

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The anthropic principle proposed by the author is discussed and clarified and compared with other versions. It is applied to an explanation of space and time. A self‐contained universe picture is constructed, which is richer than the unique universe picture, but allows the operation of the anthropic principle. It implies an intimate relation between space‐time and the quantum.
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01.70.+w Philosophy of science

Field versus action‐at‐a‐distance in a static situation

N. L. Sharma

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 420 | Cited 2 times

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The introduction of the electromagnetic field has been a necessity only in time‐varying cases. In static or steady‐state cases, it has been mostly a convenience. An example is discussed where even in static situations the field is a necessity in order to conserve angular momentum. The results are used to provide a classical picture for the electron spin in terms of the angular momentum of the associated electromagnetic field.
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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

Elastic scattering by a paraboloid of revolution

James Evans

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 423

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The differential cross section for scattering by a perfectly elastic, impenetrable paraboloid of revolution is obtained. The angular dependence is identical to that for Rutherford scattering. It follows that Rutherford scattering of particles of a particular energy is equivalent to scattering from a particular paraboloid of revolution.
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45.05.+x General theory of classical mechanics of discrete systems

Gauge invariance and quantization

Barry R. Holstein

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 425

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Quantizing theories such as quantum electrodynamics that contain a gauge invariance are discussed via a simple pedagogical example. Canonical and path integral quantization methods are compared.
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03.70.+k Theory of quantized fields
03.65.Ca Formalism
11.15.Kc Classical and semiclassical techniques

Another look at the quantum mechanical entropy of mixing

Dennis Dieks and Vincent van Dijk

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 430 | Cited 5 times

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It is often stated that the Gibbs ‘‘paradox’’ is resolved or at least alleviated in quantum mechanics because the value of the quantum mechanical entropy of mixing continuously approaches zero if the difference between the particles that are being mixed is made to vanish (i.e., if the value of the inproduct of the respective quantum states goes to one). In this article, the justification of that claim is discussed. It is pointed out that, strictly speaking, an entropy of mixing is not defined if the quantum states of the particles are no longer orthogonal. It seems, therefore, that from a fundamental point of view the Gibbs ‘‘paradox’’ is there no less in quantum mechanics than in classical statistical mechanics.
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03.65.Db Functional analytical methods
05.30.-d Quantum statistical mechanics

On cooling tea and coffee

W. G. Rees and C. Viney

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 434 | Cited 2 times

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Factors influencing the rate of cooling of hot coffee and tea have been investigated theoretically and studied experimentally using deliberately ‘‘domestic’’ apparatus. It is demonstrated that black coffee cools faster than white coffee under the same conditions. Under most (but not all) circumstances, if coffee is required to be as hot as possible several minutes after its preparation, any milk or cream should be added immediately, rather than just before drinking.
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05.70.-a Thermodynamics

A particle sliding down a movable incline: An experiment

R. E. Vermillion and G. O. Cook

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 438

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A traditional problem has a particle sliding down an incline on a movable wedge. An airtrack glider was modified to serve as such a system; the measured results for the acceleration were compared to predictions based on a model (a) neglecting friction and (b) including friction. Some experimental considerations are discussed. The system exhibits interesting features, including an angle of maximum acceleration that has a value dependent on the coefficient of friction on the incline.
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01.50.Pa Laboratory experiments and apparatus
45.05.+x General theory of classical mechanics of discrete systems

A numerical investigation of the classical motion of a particle in time‐dependent magnetic fields

Ed O’Neill and J. Garner

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 440

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Newton’s second law is solved numerically for the trajectory of a single charged particle moving in a time‐dependent spatially uniform magnetic field. The charge is restricted to a plane. Numerical results are given corresponding to several choices of time dependence of the field including a randomly fluctuating field. The induced electric field accompanying the time‐varying magnetic field is included in the equation of motion. Comments are made on the possible significance of these results to actual physical systems.
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41.60.-m Radiation by moving charges
29.27.-a Beams in particle accelerators

Numerical experiments in quantum physics: Finite‐element method

Debra J. Searles and Ellak I. von Nagy‐Felsobuki

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 444 | Cited 6 times

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A new numerical approach (finite‐element method) to solving one‐dimensional Schrödinger problems is discussed. Its effectiveness is demonstrated in solving the nontrivial finite well and Morse potential problems. Moreover, it is shown by a case study of 16 low‐lying vibrational states of Li2 that the finite‐element method can achieve the same order of accuracy more easily than the better known Numerov–Cooley method.
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03.65.Ge Solutions of wave equations: bound states

On the sign of the static susceptibility

T. M. Sanders, Jr.

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 448 | Cited 2 times

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The static electric susceptibility of a normal material is positive, and the dc dielectric constant is, correspondingly, greater than unity. The fact is noted without discussion in most books on electricity and magnetism, without remarking explicitly on causes underlying the asymmetry between the electric and magnetic properties of matter. The reason for the absence of the electric analog of diamagnetism is discussed, as well as methods for producing materials with negative static electric susceptibilities. Also demonstrated is the possibility of reversing the sign of the susceptibility of a normally paramagnetic material. Possible applications of such exotic (‘‘inverted’’) materials are considered.
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77.22.Ch Permittivity (dielectric function)
75.20.-g Diamagnetism, paramagnetism, and superparamagnetism
41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

Can a projection method of obtaining equations of motion compete with Lagrange’s equations?

Dan Scott

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 451 | Cited 4 times

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An alternative technique for deriving the differential equations of motion for problems in classical mechanics is presented. This approach can be used to derive all the same equations of motion that can be derived by use of Lagrange’s equations. Advantages of this method are its ease of derivation, its intuitive nature, the physical insights it gives, and the fact that it is somewhat more general than Lagrange’s equations. In order to properly illustrate the use of the method, several examples are shown.
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45.05.+x General theory of classical mechanics of discrete systems

Analytic approximation for the chemical potential of an ideal boson system

V. C. Aguilera‐Navarro and G. A. Estévez

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 456 | Cited 1 time

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The expansion in Dirichlet series for the Bose–Einstein integral function is reverted to find the fugacity of the system. The ensuing result and the Padé approximant technique are judiciously blended for determining a simple and accurate expression for the reduced chemical potential of a boson system, valid for arbitrary values of the Bose–Einstein integral.
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05.70.Ce Thermodynamic functions and equations of state

Rounded spikes of kompeitoh and scaling relations

Nobuyuki Murai and Tomoichi Nakata

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 459 | Cited 2 times

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Kompeitoh is sugar candy, a piece of which has many remarkable rounded spikes. A one‐dimensional model of kompeitoh is presented using the Monte Carlo method to investigate how the spikes develop in the production process. Scaling relations are revealed, which ensure approximate geometrical similarity in its growth. Its shape is expected to be round without spikes after enough time has elapsed.
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61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
02.40.-k Geometry, differential geometry, and topology

Moments of probability distribution, wavefunctions, and their derivatives at the origin of N‐dimensional central potentials

Aparna Ray, Kalyaneswari Mahata, and Pritam P. Ray

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 462 | Cited 4 times

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Generalized virial theorems are developed for central potentials in an N‐dimensional space. The virial relations are then used to find the various spatial moments of the probability distribution, wavefunctions, and their derivatives at the origin of Coulomb and isotropic harmonic oscillator potentials in N dimension.
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03.65.Ge Solutions of wave equations: bound states
03.65.Fd Algebraic methods
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A further note on unconventional Gaussian surfaces

James L. Monroe

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 465

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Abstract Unavailable
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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

Determination of Avogadro’s number (An experiment)

S. I. Salem, T. Boughter‐Cardin, M. T. Civalleri, J. W. Leonard, R. A. Schreiman, and G. A. Williams

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 466

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
06.20.Jr Determination of fundamental constants
61.05.cp X-ray diffraction

A cylindrical variation on the brachistochrone problem

H. A. Yamani and A. A. Mulhem

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 467 | Cited 1 time

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

Comments on ‘‘Extending relativity via the perplex numbers’’ [Am. J. Phys. 54, 416 (1986)]

William Band

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 469 | Cited 1 time

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Abstract Unavailable
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02.30.-f Function theory, analysis

A consolidated diagram concerning the propagation of a uniform plane electromagnetic wave that is linearly polarized

Lance Breger and James R. Kern

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 470

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Abstract Unavailable
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03.50.De Classical electromagnetism, Maxwell equations
41.20.Jb Electromagnetic wave propagation; radiowave propagation

Erratum: Correction for ‘‘A Critical Examination of the Abraham–Lorentz equation for a radiating charged particle’’ [Am. J. Phys. 55, 1017 (1987)]

J. L. Jiménez and I. Campos

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 471

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Abstract Unavailable
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41.60.-m Radiation by moving charges
03.50.De Classical electromagnetism, Maxwell equations
99.10.Cd Errata
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An optical attenuation apparatus

Richard B. McMullen, Jr. and Richard A. Bartels

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 472

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
42.25.Bs Wave propagation, transmission and absorption

Air tables and the mystery of the lost momentum

F. C. Peterson

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 473 | Cited 1 time

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
45.05.+x General theory of classical mechanics of discrete systems

A lens‐free optical image‐processing device

Achim M. Loske, Victor M. Castaño, and Alfredo Gómez

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 475

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Abstract Unavailable
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42.30.Va Image forming and processing
42.30.Wb Image reconstruction; tomography

Simple demountable Helmholtz coils

P. N. Murgatroyd and M. Belloufi

American Journal of Physics -- May 1988 -- Volume 56, Issue 5, pp. 478 | Cited 1 time

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Abstract Unavailable
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84.32.Hh Inductors and coils; wiring
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