Volume 57, Issue 9, September 1989
 Editorial


Editorial: A brief description of the editorial procedures of the American Journal of Physics
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 Papers


An introduction to generalized functions and their application to static electromagnetic point dipoles, including hyperfine interactions
View Description Hide DescriptionThe Dirac δ function, the Heaviside step function, and all their derivatives are examples of g e n e r a l i z e d f u n c t i o n s, also called d i s t r i b u t i o n s. The mathematical theory of generalized functions provides a useful framework for the description of the potentials and fields occurring in electromagnetic theory. It allows for greater clarity and applicability than that given by ordinary functions, especially where point charges and point dipoles are concerned. The present article provides a logical tutorial presentation of the relevant material. Maxwell’sequations for static point sources are reinterpreted in terms of potentials and fields that are generalized functions. Dipolar interactions are discussed in terms of these. Specifically, as an example, the hyperfine spin Hamiltonian for a 1‐electron system is considered in some detail.

The case of the identically accelerated twins
View Description Hide DescriptionA variation on the ‘‘twin paradox’’ of special relativity is presented wherein twins undergo the same acceleration for the same length of time, yet they age differently. Although this problem is simple to solve, it gets to the heart of the behavior of clocks in special relativity and, hopefully, will help to dispel the notion students develop that the acceleration experienced by a relativistic traveler is directly related to the rate at which that traveler ages.

Early diamond making at General Electric
View Description Hide DescriptionThis is an account of how GE’s early interest in a new super‐hard metal, cobalt cemented tungstencarbide, for drawing tungsten lamp filament wire, led to a broader interest in the realm of super pressure and to diamond synthesis. P. W. Bridgman at Harvard University had demonstrated the new metal’s (‘‘Carboloy’’) ability to generate pressures of 100 000 atm (100 kbars). Armed with this new capability, GE initiated a diamond project in 1951. In December 1954 two synthesized diamonds emerged in a marginal experiment that for a while could not be reproduced. Nevertheless, that experiment gave the critical clue to the process that now provides 90% of the world’s industrial diamond needs. The high‐pressure high‐temperature process (HPHT) together with the new carbonvapor deposition process (CVD) brings diamonds’ unique and valuable properties to applications requiring crystals tailored to fit specific needs.

The oscillation of the synodic period of the Moon: A ‘‘beating’’ phenomenon
View Description Hide DescriptionThe synodic period of the Moon (the period of the phases or the time from, say, full moon to full moon) exhibits oscillations about its mean value of 29.530 59 days which immediately suggest a ‘‘beating’’ between at least two frequencies. A Fourier analysis can provide some insight into the causes of the oscillation without the complexity of rigorous lunar theories. Such a Fourier approach is quite appropriate for undergraduate students of physics and astronomy, but, of course, is no substitute for more rigorous lunar theory. Fourier analysis suggests the periods of the beating frequencies to be 411 and 366 days. The 411‐day period arises since this is the time it takes the Sun to return to a similar orientation along the line of apsides (the major axis) of the lunar orbit. The 366‐day period is about a year or the time it takes the Earth to orbit the Sun. Since the lunar phases occur because of the relative orientation of the Earth, Moon, and Sun, an annual period might also be anticipated. The beat period of 3293 days is half the saros eclipse cycle period of 6585.3 days. Alternating lunar and solar eclipses are separated by the beat period. Higher frequency effects are apparent from the data, but not from the elementary Fourier approach. Thus this procedure must be used with caution in analyzing complex periodic data in astronomy.

A computer‐assisted approach to learning physics concepts
View Description Hide DescriptionA study is described that tested the effectiveness of computer‐assisted tutorial modules in dispelling common student misconceptions in first‐year mechanics. Most of the subject matter for the tutorial modules was based on examples drawn from kinematics and dynamics, which one would find on many first‐year physics tests. One of the examples, involving qualitative comparison of speeds of two differently moving objects, has been the subject of investigations of student misconceptions conducted by other workers. The present study involved a total of 96 student volunteers drawn from all of our first‐year physics courses. The results of the study suggest that computer‐assisted tutorials of the kind described here can be effective in teaching material that presents conceptual difficulties, and is often not learned directly from textbooks or from lectures delivered to large classes.

Coherent states and accidental degeneracy for a charged particle in a magnetic field
View Description Hide DescriptionThe coherent state solution for a charged particle in a constant magnetic field and its implication for the accidental degeneracy present in the problem are discussed. Furthermore, a simple derivation is given for the density of electrons per unit area in the plane perpendicular to the magnetic field, which is required for the understanding of the quantum Hall effect.

A computer‐assisted free‐fall experiment for the freshman laboratory
View Description Hide DescriptionA robust apparatus, which includes a microcomputer to control the release of a body, perform the necessary timings, and measure its average speed, is used by freshman students to study free‐fall motion. A procedure is suggested that enables students in one laboratory period to collect data to find ‘‘g’’ from least‐squares fits of the functions s=v _{0} t− 1/2 g t ^{2}, v=v _{0}−g t, and v ^{2}=v ^{2} _{0}−2g s.

Clausius–Mossotti effects: Classical and quantum mechanical approaches
View Description Hide DescriptionClausius–Mossotti effects are a consequence of the fact that a polarizable center in a dielectric does not see its own field. A derivation of this local field correction, in which its physical origin is most evident, is performed in a classical context. It is shown how in a quantum mechanical approach the Clausius–Mossotti correction in crystalline dielectricsolids is implicitly taken into account if the energy gap of the solid is used rather than the atomic energy gap.

Kramers–Kronig in two lines
View Description Hide DescriptionA short derivation of the Kramers–Kronig relations is presented.

The Compton effect as an experimental approach toward relativistic mass
View Description Hide DescriptionA way of presenting an experiment on the Compton effect to undergraduate students is suggested. First, a nonrelativistic analysis of this effect accompanied by an excellent approximation to the resulting nonrelativistic scattering formula is made. It is then shown how the discrepancy between the nonrelativistic predictions and the experimental results leads in a fairly plausible way to the relativistic form of the energy conservation law, the relativistic mass–velocity dependence, and even the formula ΔE=Δm c ^{2} .

Measuring solar luminosity with a photodiode
View Description Hide DescriptionThis article describes a simple method suitable for an undergraduate laboratory to measure solar luminosity with a photodiode. Using an uncalibrated photodiode, the results of this method are typically accurate to about 10%. Corrections are required for the photodiodespectral response along the solar Planck curve, and for the sunlight absorbed in the Earth’s atmosphere. A value for the solar constant may also be obtained.

A generalization of the Ehrenfest urn model
View Description Hide DescriptionThis article presents a generalization of the Ehrenfest urn model in order to obtain the time evolution of the number of molecules n(t) in any subvolume V of a vessel V _{0} containing N molecules of a gas. The formalism makes use of the equilibrium (stationary) probability distributionP _{ N }(n,V,V _{0})≡P _{0}(n) characterizing the gas. Two cases of pedagogical value, the ideal gas (binomial distribution) and the lattice gas (hypergeometric distribution) are considered.

Solutions to time‐harmonic Maxwell equations with a Hertz vector
View Description Hide DescriptionThe physical solutions to time‐harmonic Maxwell equations for arbitrary sources in vacuo and for arbitrary media are formulated with a single Hertz vector. It is shown that in the special case of magnetic dielectrics the formulation is equivalent to the traditional approach with an electric and a magnetic Hertz vector. The formalism is illustrated with an integral‐equation analysis of reflection from a semi‐infinite conducting dielectric.
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 Papers


Photogates: An instrument evaluation
View Description Hide DescriptionThe effective length of a flag executing photogate transit varies from photogate to photogate. It also varies with the position in the gap where it crosses the beam, and with the speed of the flag. Measurements were made using 23 photogates (the PASCO model 9204 and its newly updated version, the model 9204A). The flags were 11.66‐mm‐diam cylinders. The effective length of these flags was found to vary from photogate to photogate by up to 20%; vary with gap position by up to 8%; decrease by about 0.2% per meter/second with flag speed. Measurements and analysis are presented along with suggestions for minimizing systematic errors when using photogates in the laboratory.

A thermometer based on Archimedes’ principle
View Description Hide DescriptionThe theory is given for a thermometer whose thermometric property is the response of neutrally buoyant objects to the temperature‐dependent density of a fluid. It is found that such a device would require very careful adherence to accurate density measurements of the responding elements.

Long‐buried dismantling of a centuries‐old myth: Newton’s P r i n c i p i a and inverse‐square orbits
View Description Hide DescriptionThe author’s 1982 report of the fallacy inherent in Newton’s treatment of inverse‐square orbits in the P r i n c i p i a was anticipated by Ferdinand Rosenberger in his 1895 book‐length study of Newton’s life and work [I s a a c N e w t o n u n d S e i n e P h y s i k a l i s c h e n P r i n c i p i e n (Barth, Leipzig, 1895)]. A new alternative formulation of the case against the P r i n c i p i a treatment is offered as surpassing in effectiveness that of Rosenberger and the essentially equivalent 1982 formulation by the author. Also offered is exposure of a long‐enduring misrepresentation of a portion of the P r i n c i p i a that deals with inverse‐square orbits.

Absorption spectrum of iodine vapor—An experiment
View Description Hide DescriptionThe absorptionspectrum of iodine was photographed in the visible region using a 3.4‐m Ebert plane‐grating spectrograph. An evacuated glass envelope containing a small amount of iodine was used as the absorption cell while a tungsten filament lamp served as the continuous source. A number of band heads were identified and these measurements led to the determination of the dissociation limit, the dissociation energy, the force constant, and the fundamental vibrational frequency of the iodine molecule. Such an experiment will provide the physics major with an introduction to molecular spectra and, in light of the discovery of molecular lasers, it is recommended that such an experiment be included in the undergraduate physics curriculum.
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 Notes and Discussions


Diffraction intensity of a phase grating submerged in different liquids
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 Apparatus Notes


Measuring momentum without the use of p=m v in a demonstration experiment
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