Volume 50, Issue 8, August 1982
 Letters To The Editor



Is physics really useful?
View Description Hide Description 
Letter to the Editor
View Description Hide Description 
Letter to the Editor
View Description Hide Description 
Letter to the Editor
View Description Hide Description  Top

 Papers


How good are the common approximations used in physics?
View Description Hide DescriptionThe qualities (relative errors) of several of the common approximations used in undergraduate physics are studied. Some novel features of the approximations are discussed. In some cases it is found that the approximations are substantially better than is usually thought to be the case.

An investigation of CAI teaching methods in an electronics course
View Description Hide DescriptionComputers are increasingly being used in the classroom. An investigation of several educational techniques in a computer‐based version of an electronics course is reported. We found that, with a lesson for teaching virtual equality, students learned faster when using a general to specific approach. Students using a simulation of a Schmitt trigger before a qualitative analysis of the circuit performed the analysis faster and with less difficulty than the group performing the analysis first and then exploring the circuit with the simulation. Given a sizable amount of optional material in a computer lesson, most of the electronics students used all of the optional material.

Poincaré gauge in electrodynamics
View Description Hide DescriptionThe gauge presented here, which we call the Poincaré gauge, is a generalization of the well‐known expressions φ = −r⋅E_{0} and A = 1/2 B_{0}×r for the scalar and vector potentials which describe static, uniform electric and magnetic fields. This gauge provides a direct method for calculating a vector potential for any given static or dynamic magnetic field. After we establish the validity and generality of this gauge, we use it to produce a simple and unambiguous method of computing the flux linking an arbitrary knotted and twisted closed circuit. The magnetic flux linking the curve bounding a Möbius band is computed as a simple example. Arguments are then presented that physics students should have the opportunity of learning early in their curriculum modern geometric approaches to physics. (The language of exterior calculus may be as important to future physics as vector calculus was to the past.) Finally, an appendix illustrates how the Poincaré gauge (and others) may be derived from Poincaré’s lemma relating exact and closed exterior differential forms.

Paradox in the classical treatment of the Stern–Gerlach experiment
View Description Hide DescriptionMost textbook authors assume that the force on a magnetic moment sent into a Stern–Gerlach apparatus, is exclusively in the direction of the magnetic field. Hence they conclude that classically one should expect a continuous distribution of particles along a line in the field direction, on a screen placed behind the apparatus. However, it is easily shown that, because the divergence of the field is zero, there is in fact an equally large force t r a n s v e r s e to the field direction. This would lead to an i s o t r o p i c distribution of particles on the screen, in contradiction to the above conclusion. The paradox is resolved by taking into account the t o r q u e on the magnetic moment. This produces a rapid precession about the field direction, causing the transverse force to average out and thus giving the usual textbook result.

Hyperfine splitting in the ground state of hydrogen
View Description Hide DescriptionThe hyperfine structure of atomic hydrogen is derived in a simple and self‐contained way that makes the theory accessible to advanced undergraduates in a first course on quantum mechanics.

Local‐field effects and effective‐medium theory: A microscopic perspective
View Description Hide DescriptionStandard textbook derivations of the Clausius–Mossotti (Lorentz–Lorenz) relation tend to obscure the physical origin of local‐field effects by proceeding from the macroscopic dielectric function of the equivalent homogeneous system to the microscopic parameters of the model. The microscopic and macroscopic aspects can be made clearer by reversing the order, that is, by first obtaining the microscopic solution and then implementing the definition of macroscopic quantities as averages of their microscopic counterparts. This approach also leads naturally into a treatment of effective‐medium theory and the description of the dielectric response of heterogeneous materials.

Nuclear spins in the Earth’s magnetic field
View Description Hide DescriptionDetails are given of a simple apparatus for the observation of nuclear precession in the Earth’s magnetic field.Spin echos are generated using a pulse of oscillatory magnetic fieldresonant at the Larmor frequency. Students can use the system to measure a nuclear magnetic moment, nuclear relaxation times, and the local strength and orientation of the Earth’s magnetic field.

Science and society test VII: Energy and environment
View Description Hide DescriptionApproximate numerical estimates are developed in order to quantify a variety of environmental effects that result from energy production. The results of these calculations are consistent with either direct observations or with more complex calculations. This paper will cover some of the possible environmental effects of the following: (1) the greenhouse effect caused by increased CO_{2} in the atmosphere; (2) loss of coolant accidents in nuclear reactors; (3) increased radon concentrations in buildings with very low air infiltration rates; (4) acid rain from the combustion of fossil fuels; (5) expolosions of liquified natural gas (LNG); and (6) ozone in the stratosphere.

Dirac’s light‐cone coordinate system
View Description Hide DescriptionIt is shown that Dirac’s light‐cone coordinate system provides an effective method for treating the geometry of Lorentz transformation in a rectangular coordinate system. Transformation properties of the coordinate variables and those of the derivatives are discussed in detail. The Lorentz boost along a given direction is shown to be a coordinate transformation in which ’’cross products’’ are preserved. It is pointed out that the Lorentz boost is a symplectic transformation.

Teaching problem‐solving in physics: A course in electromagnetism
View Description Hide DescriptionIn order to improve the teaching and learning situation in the course Electromagnetism for first‐year students at the Twente University of Technology, this course has been reconstructed. The main activity in the reconstruction has been directed towards developing means and instructional procedures helpful to the students in learning how to tackle problems in electromagnetism. Therefore a model of the process of solving such problems has been developed and a system of actions and methods appropriate to this problem solving has been derived from the model. On the basis of the learning and instruction theory of Gal’perin this system has been incorporated in the instructional procedures of the course. The results of the reconstructed course as shown in the examination scores have improved compared to previous courses.

Sudden loss of mass from a binary gravitating system
View Description Hide DescriptionA recent discussion by Mitalas is generalized to treat sudden mass loss from a binary system in an originally e l l i p t i c a l orbit. Emphasis is placed on characterizing the orbits by angular momentum and energy, and it is shown that none of the changes in the r e l a t i v e orbit depends on which object loses part of its mass; indeed, in principle, each could lose a different fraction. Time averages are introduced so that the orbital changes, which depend on w h e r e in orbit the mass loss occurs, can be suitably averaged over a statistical ensemble of initial systems. Although I present several results that appear to be new (such as a unique relation between the increase in the semimajor axis and the change in eccentricity, independent of the orbital phase at the moment of mass loss), the main thrust is to choose and manipulate variables yielding the greatest economy of description and the greatest power of computation. (All calculations were easily done on a pocket calculator.) Graphs are presented showing the fraction of systems that on the average will be disrupted, the mean orbital changes for the survivors (which can easily turn out to have s m a l l e r mean eccentricity than the progenitors), and the extreme limits for the change in eccentricity.

Actions at a distance, four‐dimensionality, and the problem of ’’where is the energy?’’
View Description Hide DescriptionAn argument traditionally used against action‐at‐a‐distance theories is that for such theories one cannot find a ’’reasonable’’ statement of conservation of energy because ’’where is the energy?’’Using as an example Fokker’s electrodynamics, we argue against such an objection, showing that it is possible to construct a model in which the question ’’where is the energy?’’ is answered. We also relate this problem to the question of the formal character of conservation laws.

The connection between the charged‐particle current and the displacement current
View Description Hide DescriptionIn Ampère’s circuital law, two separate terms are required to describe the contributions to the magnetic field of the charged‐particle current and the ’’displacement current.’’ In this paper, it is shown how both terms arise by applying the Biot–Savart law to a calculation of the displacement current resulting from the motion of a single charged particle. The conclusions drawn from this calculation are applied to the case of a steady straight current filament.

Propagation of an electromagnetic wave in a slowly moving conducting dielectric
View Description Hide DescriptionThe effect of conductivity on the propagation of an electromagnetic wave in a moving medium is considered and a modified form of the Fresnel formula is obtained. The effect is shown to be negligible for light waves for the usual experimental situations. Some relative properties of the fields and briefly considered.

Isospin relations by counting
View Description Hide DescriptionA method is given for finding the relations between reaction cross sections or decay branching fractions that result from isospin conservation. The method was discovered long ago by Shmushkevich but is not widely known. It makes no call on the usual machinery of amplitude expansions and Clebsch–Gordan coefficients, but works instead by apportioning certain populations of particles according to a simple counting rule, the charge‐uniformity rule. A number of examples, including several that require lengthy calculation to solve using Clebsch–Gordan coefficients, are here solved by inspection, usually without any equations at all.
