December 2024
Volume 92, Issue No. 12
Teaching magnetism with bivectors
The magnetic field is traditionally presented as a (pseudo)vector quantity, tied closely to the cross product. Though familiar to experts, many students find these ideas challenging and full of subtleties. Building on earlier work in rotational physics, we present an alternative pedagogical approach that describes magnetic fields using bivectors. These objects can be visualized as oriented tiles whose components form an antisymmetric matrix. Historically, bivectors have been mostly used in specialized contexts like spacetime classification or geometric algebra, but they are not necessarily more complicated to understand than cross products. Teaching magnetism in this language addresses common student difficulties, generalizes directly to relativity (and extra dimensions), and brings fresh insight to familiar ideas.
EDITORIAL
In this issue: December 2024 by Jesse Kinder; Beth Parks; Donald Salisbury; Todd Springer; Keith Zengel. DOI: 10.1119/5.0245536
LETTERS TO THE EDITOR
An undergraduate entryway into experimental particle physics by Mark Lattery; Sean Dobbs; Grant Lattery. DOI: 10.1119/5.0214640
On Heisenberg and the bomb by B. Cameron Reed. DOI: 10.1119/5.0240112
AWARDS
2024 David Halliday and Robert Resnick Award for Excellence in Undergraduate Physics Teaching Lecture: It's not business, it's personal. Teaching large classes, one student at a time by Tatiana Erukhimova. DOI: 10.1119/5.0243729
Editor's Note: This paper is the text of a plenary talk given by the author at the AAPT Summer 2024 meeting when she accepted the David Halliday and Robert Resnick Award for Excellence in Undergraduate Physics Teaching.
2024 Jackson Award for Excellence in Graduate Physics Education lecture: Physics graduate education for the 21st century by Chandralekha Singh. DOI: 10.1119/5.0242316
Editor's Note: This paper is the text of a plenary talk given by the author at the AAPT Summer 2024 meeting when she accepted the J.D. Jackson Award for Excellence in Graduate Physics Education.
PAPERS
Scattering shadows by Thomas Curtright; Gaurav Verma. DOI: 10.1119/5.0208720
Editor's Note: This article presents an intuitive approach to infinite cross sections by way of the “scattering shadow” of a repulsive potential. The authors apply classical scattering theory to repulsive power-law and Yukawa potentials, present numerical methods for calculating the envelope of trajectories that define the shadow, and derive analytic expressions for its asymptotic behavior. Scattering shadows clearly illustrate the physical origin of infinite cross sections. As such, the approach complements traditional analyses of scattering cross sections based on the impact parameter or differential cross section, common in texts and courses on classical scattering and quantum mechanics.
Energy density of any capacitor or inductor by Jinliang Zheng; Shang-Yuu Tsai. DOI: 10.1119/5.0220501
Editor's Note: The authors present a clever derivation of the static electric and magnetic field energy densities for capacitors and inductors of any shape. The derivations generalize the simple and often discussed cases of infinite parallel plate capacitors and infinitely long solenoids while requiring only a conceptual understanding of integral vector calculus. The discussion is suitable for introductory physics courses and will be of interest for teachers seeking new ways to introduce the challenging concept of field energy density.
Teaching magnetism with bivectors by Steuard Jensen. DOI: 10.1119/5.0176852
Editor's Note: For many reasons, magnetism is extremely challenging for the introductory physics student. Magnetic forces are non-intuitive and jarringly different than electric forces. Problems involving magnetism traditionally require three-dimensional reasoning, cross products, and right-hand rules. It is natural to wonder whether new teaching approaches can help students learn such a difficult subject. Building on earlier work in rotational physics, this article explores a non-traditional pedagogical approach where bivectors (represented by oriented tiles) are used to teach magnetism. This fresh perspective may help students avoid pitfalls associated with the traditional approach, while also preparing them for more advanced discussions of relativistic electromagnetism.
Why is there no Poisson spot in a solar eclipse? by Jami J. Kinnunen. DOI: 10.1119/5.0227357
Editor's Note: The question asked in this paper's title falls in the category of “Why didn't I think to ask that?” It is answered in just the way that you will want to answer it in a class: first with an experimental demonstration that larger objects result in smaller and dimmer Poisson spots, followed by a simple calculation, and then completed with a more careful calculation that is still not too hard to present in class. This seems to be appropriate for an introductory or intermediate optics course.
Completeness of energy eigenfunctions for the reflectionless potential in quantum mechanics by Fatih Erman; O. Teoman Turgut. DOI: 10.1119/5.0228452
Editor's Note: The reflectionless potential, also called the Pöschl–Teller potential, is one of the less-often discussed quantum potentials with known analytical solutions. The system has many interesting properties, including the fact that it allows both bound and scattering states and that the potential well never reflects incident particles. The authors here present new ways to think about the somewhat counter-intuitive completeness of the set of bound and scattering states of the system.
Counterintuitive properties of relativistic relative motion for accelerated observers by M. Pössel. DOI: 10.1119/5.0203454
Editor's Note: Could a laser rangefinder give constant readings even though the distance between two objects is changing? Will two observers always agree about whether they are moving toward each other or away from each other? This paper analyzes accelerating observers within the frameworks of Newtonian physics and special relativity to reveal how classical intuition about such questions can lead one astray. The author then demonstrates how accelerated motion in special relativity can provide insight into gravitational redshifts and event horizons in general relativity. Only algebra and calculus are used in the analysis, making these intriguing “paradoxes” accessible to students in modern physics or a first course in relativity.
Hyperbolic times in Minkowski space by Anıl Zenginoğlu. DOI: 10.1119/5.0214271
Editor's Note: The finite spacetime manifold in which outgoing waves reach infinity in a finite spacetime interval was introduced in the 1960s by Roger Penrose. It plays an important role in the analysis of gravitational waves. In this work the author shows how to construct a temporal foliation using spacelike slices with hyperbolic geometry in compactified Minkowski space. Instructors in special relativity will be able to make these ideas accessible to their students, including an application to massless fields in flat spacetime.
NOTES AND DISCUSSIONS
Exact solutions for the inverse problem of the time-independent Schrödinger equation by Bhavika Bhalgamiya; Mark A. Novotny. DOI: 10.1119/5.0172824
Editor's Note: Solving the Schrödinger equation to find energies and wave functions is hard, so in the classroom, we're normally limited to a few potentials that have analytical solutions. This paper turns the problem around: what if you start with a wave function and ask what potential this solves? Use this idea to generate some new problems for your undergraduate or graduate quantum mechanics course.
The field inside an infinite solenoid of arbitrary cross section using Ampère's law by Ian C. Malcolm. DOI: 10.1119/5.0215691 Editor's Note: This brief note shows how symmetry arguments can be used to find the B-field of an infinite solenoid with a non-circular cross section and includes a review of how the pseudovector B behaves on reflection.
Comment on “Determining the difference between local acceleration and local gravity: Applications of the equivalence principle to relativistic trajectories” [Am. J. Phys. 92(6), 444–449 (2024)] by Frank Wang. DOI: 10.1119/5.0227213 Editor's Note: A straightforward approximate algebraic procedure for introducing locally flat coordinates in a Schwarzschild spacetime is undertaken in this Comment on the recent leading order differential approach elucidated by Steven Balbus in the June 2024 issue. It is very likely that instructors even in special relativity could employ this technique and thereby obtain the correct deflection angle for light in an accelerated frame of reference.
Erratum: “Fraunhofer diffraction by a thin wire and Babinet's principle” [Am. J. Phys. 73, 83–84 (2005)] by Salvatore Ganci. DOI: 10.1119/5.0238915
Additional Resources
 |