Volume 45, Issue 10, October 1977
 Papers


Physics teaching as a laboratory experiment
View Description Hide DescriptionA novel method has been employed at the Technion to expose senior physics students to physics teaching. Students were allowed to substitute for one three‐week laboratory experiment, an ’’experiment in teaching physics.’’ The setting for the experiment was the eigth grade class of an unsophisticated Israeli village. The experiment provided a remarkably stimulating experience for the students, the pupils, and the elementary teachers. The experience even changed the career goals of a number of the students involved.

Computer‐graded homework in introductory physics
View Description Hide DescriptionComputer‐graded multiple‐choice problem sets provide some of the advantages of homework graded in a traditional manner. Solution sheets for each set provide a solution to each problem and hints which will help the student identify his misconceptions.

Einstein’s comprehensive 1907 essay on relativity, part III
View Description Hide DescriptionThis is the concluding part of the English rendition of Einstein’s 1907 essay on relativity, of which part I appeared in the June 1977 issue of this Journal and part II in the September 1977 issue. It consists of a direct translation of the last part of the essay, part V, entitled ’’Principle of Relativity and Gravitation,’’ and of a few added footnotes.

What is the principle of equivalence?
View Description Hide DescriptionThe strong principle of equivalence is usually formulated as an assertion that in a sufficiently small, freely falling laboratory the gravitational fields surrounding the laboratory cannot be detected. We show that this is false by presenting several simple examples of phenomena which may be used to detect the gravitational field through its tidal effects; we show that these effects are, in fact, local (observable in an arbitrarily small region). Alternative formulations of the strong principle are discussed and a new formulation of strong equivalence (the ’’Einstein principle’’) as an assertion about the field equations of physics, rather than an assertion about all laws or all experiments, is proposed. We also discuss the weak principle of equivalence and its two complementary aspects: the uniqueness of free fall of test particles in arbitrary gravitational fields (’’Galileo principle’’) and the uniqueness of free fall of arbitrary systems in weak gravitational fields (’’Newton principle’’).

A low‐cost experiment in plasma physics for the advanced undergraduate lab
View Description Hide DescriptionA quantatative experiment in plasma physics requiring only a modest investment is presented. The plasma source is a seeded propaneflame. The object of the experiment is to measure the characteristics of a cylindrical Langmuir probe and the ion density in the flame plasma.

Determination of a planet’s diameter by occultation time—an introductory astronomy exercise
View Description Hide DescriptionThis paper describes an exercise developed for a liberal arts astronomy course in which the students obtain values for the diameter of Venus by timing the intervals between contacts in a videotaped occultation of that planet by the Moon. Approximate expressions relating the planetary diameter to this time interval are obtained for occultations of a planet in the crescent or gibbous phases. We note that classroom playback of certain videotaped astronomical events demonstrates clearly their dynamic nature.

Method for solving electrostatic problems having a simple dielectric boundary
View Description Hide DescriptionElectrostatic problems having a simple dielectric boundary are solved using the concept of polarization charge. Using elementary mathematics, it is shown that the electrostatic field due to the total polarization charge distributed on a boundary surface between two homogeneous and isotropic dielectrics, is equivalent to that due to the lumped image charge used conventionally in teaching these problems. The demonstration of the equivalence of the surfacepolarization charge to the image charge will help students to understand the physical base of the image charge. Two problems are treated: a plane dielectric boundary, and a dielectric sphere immersed in a uniform field.

Polarization of a polar gas by external and internal electric fields
View Description Hide DescriptionLinear‐polar molecules in an external field contribute to two kinds of polarization effects which may be described in classical terms. First, the external field E produces a torque on each molecule which tends to align its electric dipole moment μ in the direction of the field. At high temperatures the average alignment energy is 〈μ⋅E〉=−μ^{2} E ^{2}/3k T. Second, each molecule experiences an internal electric field due to nearby molecules which tends to align the dipole moment of a molecule along the internal field it experiences. This results in an average attractive interpair potential energy 〈U〉=−2μ^{4}/3r ^{6} k T. A method of estimating 〈U〉 is described, which is based on the division of molecules into two classes, ’’slow’’ or ’’fast’’, according to their rotational speed. This approach can also be used to estimate 〈μ⋅E〉. Results for a three‐dimensional gas are contrasted with those for a two‐dimensional gas, and the approach to equilibrium of 〈μ⋅E〉 for a two‐dimensional gas is described in detail.

Diffraction of a δ‐function pulse at a half plane: the boundary pulse
View Description Hide DescriptionThe diffraction of a plane δ‐function pulse by a black half plane is treated by Stokes’ diffraction formula. The solution is a superposition of the incident pulse terminated at the geometric shadow boundary and a separate cylindrical boundary pulse exhibiting diffusion. The boundary pulse satisfies Lamb’s theorem, and its Fourier transform yields the monochromatic boundary wave. The mathematical reason for the π/4 phase shift is seen in the Fourier transform of the pulse tail. The character of the solution is sufficient to show that the boundary pulse originates at the edge of the diffracting aperture, and to illustrate clearly the kinematical aspects of diffraction at a black screen.

Time‐dependent scattering of wave packets in one dimension
View Description Hide DescriptionThis paper treats the scattering of wave packets in one space dimension at the mathematical level of the first‐year graduate student. The analytic properties of the general‐scattering solutions are emphasized, thereby making the analysis useful as introductory material for a more sophisticated S‐matrix treatment. Resonant scattering, time delay, and line shape, as well as the relationship between bound and resonant states, all follow as a natural consequence of the analysis.

Bose particles in an external electromagnetic field as a one‐particle problem
View Description Hide DescriptionThe statement is often made that the second quantized Hamiltonian for a system of noninteracting particles in an external weak electromagnetic field gives rise essentially to a one‐particle problem, to which there corresponds a dressed vacuum different from the bare one. In this paper we implement that statement by explicitly constructing the dressed vacuum, together with the quasiparticle creation and annihilation operators associated with the one‐particle problem. The process of diagonalizing the Hamiltonian is illustrated step by step in a simple model.

Color centers: An example of a particle trapped in a finite‐potential well
View Description Hide DescriptionThe wavelengths for color‐center absorption can be determined from a simple quantum‐mechanical model consisting of an electron trapped in a square finite‐potential well. By varying the depth and width of this well we are able to adjust this model so that it predicts Ivey’s relationship [λ (Å) =73a ^{1.80}] between the F‐center wavelength λ and the nearest‐neighbor lattice spacing a. A more complicated model based on a spherical finite‐potential well is also used to obtain Ivey’s law. The depth and width of the well that fit this latter model to the F‐center absorption data are then used to predict the wavelengths for the K, L, L _{2}, and L _{3} centers to −6%, 4.5%, 1.5%, and −1.0% respectively.

A simple field theoretic description of photon interference
View Description Hide DescriptionA description of photon‐interference experiments of the Young’s type using the techniques of quantum‐field theory is presented. In particular, an explicit illustration of Dirac’s statement that a photon interferes only with itself is given. The interference patterns produced by a one photon, an nphoton and a coherent photon field are calculated. A discussion of the degree of optical coherence possessed by the above fields is also incorporated. by the above fields is also incorporated.

A simple demonstration on the freezing of the rotational energy of molecular hydrogen
View Description Hide DescriptionThe specific heatC _{ v } of the diatomic gas H_{2} decreases from 5R/2 at room temperature to ∠3R/2 at liquid N_{2} temperature, a value typical of the translational energy only. This quantum effect can be shown in a quickly performed lecture demonstration, based on the principle of a differential H_{2}/N_{2} acoustic thermometer.

The free‐electron gas in n dimensions
View Description Hide DescriptionAn n‐dimensional free‐electron gas confined in a box is studied and the density of states is calculated explicitly. The energy and specific heat are obtained in the low‐temperature limit. Explicit expressions are given for n=1, 2, and 3.

Superposition of the radiation from N independent sources and the problem of random flights
View Description Hide DescriptionIt is often stated that the intensity of the signal produced by superposition of N equally intense, but randomly phased, monochromatic coherent waves tends to N as N becomes large. An examination (first made by Rayleigh) of the distribution of intensities obtained by superposing N independent monochromatic waves shows that the mean intensity is N and the variance is N ^{2}−N. Exploiting the analogy of this problem to random walk in two dimensions (’’random flight’’), we have recalculated the distribution for N=2 to 6 and compared it with the results from a computer experiment.

Enskog and van der Waals play hockey
View Description Hide DescriptionWe consider the mean free path of a hockey puck in a system of other pucks on an air table, and show how the simple low‐density kinetic‐theory value for this mean free path can be extended to higher densities. This approach is connected both with the Enskog theory of the transport properties of dense gases and with the van der Waals theory of the equation of state of dense gases. We derive several simple approximations for the high‐density mean free path, and compare the results with each other, with accurate computer‐simulation results, and with experimental results obtained in the freshman physics laboratory of the University of Maryland. We present the arguments in both simplified and more elaborate forms.

Electromotive force, potential difference, and voltage
View Description Hide DescriptionTechnical journals and dictionaries exhibit no uniformity regarding use of the terms electromotive force, potential difference, and voltage. Electromotive force is sometimes deprecated, and sometimes considered to be a synonym for one of the other terms. The three terms relate to different aspects of electrical phenomenona, and it is useful to draw distinctions among them and define each in a precise way.

Solar energy—its measurement
View Description Hide DescriptionThe calibration of bolometric and photoelectric devices for application to the measurement of solar energy is considered. In particular, a bolometric radiometer for measuring this energy is described. Radiometric data is compared to that obtained from a selenium photovoltaic cell.

Geometry factors for experiments in radioactivity
View Description Hide DescriptionThe problem of determining the number of radioactive particles entering a detector window of radius a from a parallel and coaxial disk source of radius b is discussed. A diagram is presented which gives the effective solid angle, or geometry factor, subtended by the detector at the source for various values of b and z, the source‐detector spacing. The range of parameters covered is a=1, 0<b<8, 1<z<5.
