Volume 79, Issue 10, October 2011
 PAPERS


Foaming in stout beers
View Description Hide DescriptionWe review the differences between bubble formation in champagne and other carbonated drinks, and stout beers which contain a mixture of dissolved nitrogen and carbon dioxide. The presence of dissolved nitrogen in stout beers gives them several properties of interest to connoisseurs and physicists. These remarkable properties come at a price: stout beers do not foam spontaneously and special technology, such as the widgets used in cans, is needed to promote foaming. Nevertheless, the same mechanism, nucleation by gas pockets trapped in cellulose fibers, responsible for foaming in carbonated drinks is active in stout beers, but at an impractically slow rate. This gentle rate of bubblenucleation makes stout beers an excellent model system for investigating the nucleation of gas bubbles. The equipment needed is modest, putting such experiments within reach of undergraduate laboratories. We also consider the suggestion that a widget could be constructed by coating the inside of a beer can with cellulose fibers.

Why is surface tension a force parallel to the interface?
View Description Hide DescriptionA paperclip can float on water. Drops of mercury do not spread on a surface. These capillary phenomena are macroscopic manifestations of molecular interactions and can be explained in terms of surface tension. We address several conceptual questions that are often encountered when teaching capillarity and provide a perspective that reconciles the macroscopic viewpoints from thermodynamics and fluid mechanics and the microscopic perspective from statistical physics.

The twopiston problem revisited: Generalization from reversible to irreversible expansion
View Description Hide DescriptionWe discuss the adiabatic twopiston problem for an ideal gas confined between two pistons of equal mass and extend recent work based on the reversible approximation. More realistic equations that account for the roles of the gas temperature and particle mass are applied to extend the analysis of the expansion of the gas from reversible to irreversible behavior to the limit of free expansion. The evolution of quantities, such as temperature, piston speed, adiabatic reversibility coefficients, and entropy, is obtained, and differences between the irreversible and the reversible solutions are investigated.

Is Newton’s second law really Newton’s?
View Description Hide DescriptionWhen we call the equationf = m a “Newton’s second law,” how much historical truth lies behind us? Many textbooks on introductory physics and classical mechanics claim that the Principia’s second law becomes f = m a, once Newton’s vocabulary has been translated into more familiar terms. But there is nothing in the Principia’s second law about acceleration and nothing about a rate of change. If the Principia’s second law does not assert f = m a, what does it assert, and is there some other axiom or some proposition in the Principia that does assert f = m a? Is there any historical truth behind us when we call f = m a “Newton’s second law”? This article answers these questions.

The refractive anamorphic viewer of J.F. Niceron: Reconstructing a 17th century optical toy
View Description Hide DescriptionWe have analyzed and reconstructed the refractive anamorphic viewer described by J.F. Niceron in his book, La Perspective Curieuse, which created a sensation in 17th century intellectual circles. We deduced the morphology of one of the polyprisms that he described, and constructed the refractive element in the apparatus. The optical elements of the apparatus were simulated using a ray tracing program to determine the parameters of the viewer so that a working replica could be constructed. The analysis is a good example of the use of mathematics and physics in a problem of art history.

Magnetic field of a finite solenoid with a linear permeable core
View Description Hide DescriptionThe integral form of Ampere’s law applied to an infinitely long solenoid gives a good first approximation to the magnetic field of finite aircored solenoids with length L to width w ratios (aspect ratios) significantly greater than 1. It is less well known that this approximation requires much larger aspect ratios to be applicable to solenoids whose relative core permeability is much greater than that of the surrounding medium. An exact expression is derived for the magnetic field and inductance of a linear permeable core spheroidal solenoid, and an inequality is obtained for the validity of the infinite solenoid approximation. It is demonstrated that the magnetic field and inductance of a spheroidal solenoid with a linear core approximate well with those of a cylindrical solenoid of the same length and width.

A first principles derivation of the electromagnetic fields of a point charge in arbitrary motion
View Description Hide DescriptionThe electromagnetic fields of an accelerated charge are derived from first principles using Coulomb’s law and relativistic transformations. The electric and magnetic fields are derived for the instantaneous rest frame of the accelerated charge, without using Gauss’s law, an approach different from that in the literature. We then calculate the electromagnetic fields for an accelerated charge in nonrelativistic motion. The expressions for these fields, supposedly accurate only to first order in the reduced velocity β, yield all terms for the acceleration fields, and are missing only a factor of 1–β^{2} in the velocity fields. The derivation shows the genesis of various terms in the field expressions when expressed in terms of the time retarded position of the charge. A straightforward transformation from the instantaneous rest frame yields expressions for the electromagnetic fields for a charge with an arbitrary velocity. The field expressions are derived without using Liénard–Wiechert potentials, thereby avoiding the evaluation of spatial and temporal derivatives of these potentials at the retarded time.

Measuring the speed of electromagnetic waves using the cross correlation function of broadband noise at the ends of a transmission line
View Description Hide DescriptionWhen one end of a transmission line is connected to a broadband noisegenerator, sharp peaks are visible in the crosscorrelation function of the signals at both ends of the line. The speed of the electromagnetic waves can be deduced from the time when the peaks appear. The method is suitable for introducing the concepts of crosscorrelation functions and noise analysis in an undergraduate physics laboratory.

A simplified approach to synchrotron radiation
View Description Hide DescriptionSynchrotron radiation is examined in a simple and pedagogical way. The approach is that of Feynman and provides an intuitive, but rigorous graphical interpretation of the distinction between true and apparent relativistic electron motion. Feynman’s demonstration that the apparent motion in the field of a bending magnet follows a curtate cycloid is augmented by a novel derivation of the emission spectrum. A similar graphical analysis is applied to insertion device radiation, to highlight the distinction between a wiggler and an undulator.

Kramers–Kronig, Bode, and the meaning of zero
View Description Hide DescriptionThe implications of causality are captured by the Kramers–Kronig relations between the real and imaginary parts of a linear response function. In 1937, Bode derived a similar relation between the magnitude (response gain) and the phase. Although the Kramers–Kronig relations are an equality, the Bode’s relation is effectively an inequality. This difference is explained using elementary examples and is traced back to delays in the flow of information within the system formed by the physical object and the measurement apparatus.

Composition of physical quantities in one dimension: Grouptheoretic differentiable functions
View Description Hide DescriptionWe show that any grouptheoretic differentiable operation in an open interval of real numbers is isomorphic to the usual addition of real numbers. Given the composition law, it is possible to establish the transformation relation. Alternatively, given a transformation, it is possible to obtain the composition relation in terms of the new variable. We show that some well known cases such as entropy and the relativistic addition of parallel velocities are included in this general framework. The composition rules for a wide variety of phenomena ranging from electrical circuits to thermodynamic systems are treated in a unified way.

Simple approach to relativistic spin dynamics
View Description Hide DescriptionSpin dynamics is considered from the point of view of relativistic classical mechanics. It is shown that the assumptions of the BargmannMichelTelegdi theory may be used to obtain an intuitive and convenient equation of motion. The advantage of this approach is that the presence of Thomas precession is automatically and manifestly demonstrated. An easy and unambiguous way to achieve the original BargmannMichelTelegdi equation is also proposed.
 Top

 PHYSICS EDUCATION RESEARCH


Student understanding of the angular momentum of classical particles
View Description Hide DescriptionStudents in introductory calculusbased physics were asked about the angular momentum of a particle traveling in a straight line. The tendency to state that the angular momentum is identically zero was widespread, and few students applied l = r × p correctly. The common errors reflect a tendency to conflate angular momentum with angular velocity or with linear momentum. Many students assume that linear and angular momentum are jointly conserved, an error that appears to be linked to their thinking about energy. A tutorial was developed to help students recognize that linear momentum and angular momentum are separately conserved. The results suggest that helping students understand why angular momentum is attributed to a particle moving in a straight line may be more effective in helping them to apply the concept than instructing them only on its correct use. In addition to providing insights into student learning of the concept of angular momentum, we illustrate how students’ own ideas can be the basis for more effective instruction.
 Top

 APPARATUS AND DEMONSTRATION NOTES


Measuring soap bubble thickness with color matching
View Description Hide DescriptionThis paper describes a laboratory experiment designed to measure thickness variations across a soap bubble. The experiment uses the phenomenon of thin film interference and the principles of color perception to measure the thickness of the soap film at various points across the surface of the bubble. The students review the classical theory of interference and use a digital camera to make the measurements. The apparatus required for the experiment is inexpensive and easy to construct. This experiment is suitable for a senior undergraduate course and can potentially be used to study hydrodynamic effects in soap films.
 Top

 BOOK REVIEWS


Coming of Age with Quantum Information: Notes on a Paulian Idea.
View Description Hide DescriptionThis article reviews Coming of Age with Quantum Information: Notes on a Paulian Idea. by Christopher A. Fuchs 
BOOKS RECEIVED
View Description Hide Description
