### April** 2023 Issue,**

**Volume 91, No. 4**

A smoke chamber and light-sheet video microscope setup is relatively easy to construct and provides opportunities for undergraduates to participate in a variety of advanced experiments, including the demonstration of Brownian motion and the interaction of induced electrostatic dipoles in aerosol particle agglomeration. We present results of these experiments along with information to allow replication of the setup in undergraduate physics laboratories. A theoretical model of the rate of aerosol agglomeration of long dipole chains as a function of electric field agrees with experiments at field strengths up to 200 kV m−1.

#### EDITORIAL

In this issue: April 2023 by John Essick, Claire A. Marrache-Kikuchi, Beth Parks and Cameron Reed

#### LETTERS TO THE EDITOR

ChatGPT: A test drive by J. Wang

A revolution in physics education was forecast in 1989, why hasn't it happened? What will it take? by William Flannery

#### PAPERS

Projectile motion with quadratic drag by John L. Bradshaw

Projectile motion with air resistance is a staple topic of dynamics courses. If the resisting force is proportional to the instantaneous speed (Stokes drag), the equations of motion can be solved explicitly for velocity and position as a function of time, but this is not possible if the force is proportional to the square of the speed (Newtonian drag); one must then invoke numerical methods. However, if the equations of motion are formulated in terms of the angle between the instantaneous velocity vector and the horizontal direction, it is possible to solve analytically for the velocity components in the case of Newtonian drag, although position components must still be obtained numerically. This paper explores this angular formulation and presents numerical examples for baseball-sized objects. Corresponding spreadsheets are made available for student use. Appropriate for intermediate-level dynamics students.

A charge analysis of non-invasive electrical brain stimulation by Maurice M. Klee

American Journal of Physics 91, 264 (2023); https://doi.org/10.1119/5.0085625 Instructors looking for new applications to teach in their electricity and magnetism courses will enjoy reading this analysis of charges and electric fields in the brain. The simple computational model can form the basis of student problems and projects and could also be used in a non-calculus-based course for students interested in biology and medicine.

Electromagnetic induction: How the “flux rule” has superseded Maxwell's general law by Giuseppe Giuliani

In the second volume of his 1873 Treatise, James Clerk Maxwell derived a general law of electromagnetic induction to explain the phenomenon discovered by Michael Faraday in 1831. However, most courses and textbooks on electromagnetism explain induction through the so-called “flux rule,” which states that the induced electromotive force in a circuit is determined by the time-variation of the magnetic flux going through the circuit (𝜀=−𝑑/𝑑𝑡∬𝐵→·𝑑𝑆−→) . However, the “flux rule” is not a physical law (it is non-local), and it isn't even true in all circumstances. Instead, Maxwell's general law is a genuine physical law, provided one considers the motion of the charge carriers, which Maxwell did not know existed. This article aims to rehabilitate Maxwell's general law and to understand why it has been mostly forgotten. Appropriate for history of science classes or for an interlude on the foundations of electromagnetism.

Modeling the frequency response of an acoustic cavity using the method of images by Frank Rice, Teresa Riedel and Isaiah Curtis

Most instructors are familiar with the method of images as a beautiful trick to solve boundary condition problems in electrostatics. But did you know that the same trick can be used to model the frequency response of a resonant cavity? This paper describes how students can measure and analyze this frequency response as part of a multi-week laboratory project. Parts of the analysis can be done fairly simply, and it can also be extended to challenge even the most advanced students.

Fundamental properties of beamsplitters in classical and quantum optics by Masud Mansuripur and Ewan M. Wright

Beamsplitters are fundamental elements of quantum optics experiments, and, as shown in demonstrations such as the Hong-Ou-Mandel interference dip, their behavior can be highly counter-intuitive (see the next paper by DiBrita and Galvez). This paper derives magnitude and phase relations between probability amplitudes and applies them to understand the behavior of photon-number states incident on beamsplitters, showing that the result is consistent with the standard treatment using photon creation and annihilation operators. This manuscript will be highly useful to teachers of quantum optics.

An easier-to-align Hong–Ou–Mandel interference demonstration by Nicholas S. DiBrita and Enrique J. Galvez

The Hong–Ou–Mandel experiment demonstrates fundamental quantum-mechanical concepts such as wavefunction symmetry and particle indistinguishability. In this quantum-optics experiment, when two photons entering separate beamsplitter input ports are made indistinguishable in all possible ways, the interference of probability amplitudes results in both photons always leaving the same beamsplitter output port. This paper presents a simplified version of the Hong–Ou–Mandel experiment that is suitable for the undergraduate instructional laboratory. The use of a fiber-coupled beamsplitter greatly simplifies the required optical alignments and waveplates and a translation stage are used to vary the distinguishability of the photons. The paper presents a theoretical description of the experimental effect at the introductory quantum mechanics level, along with a discussion of the apparatus alignment procedure.

An economical smoke chamber and light-sheet microscope system for experiments in fluid dynamics and electrostatics by Karl D. Stephan

A new idea for an advanced lab: imaging particles of MgO in a smoke chamber. An inexpensive apparatus allows students to explore Brownian motion and particle agglomeration, and it could be extended to other topics such as laminar and turbulent flow. This laboratory exercise would be especially interesting for astronomy students who are studying the process by which particles clump together in the early stages of planet formation. A video abstract accompanies the online version of this paper.

Eccentricity and orientation of Earth's orbit from equinox and solstice times by B. Cameron Reed

The eccentricity of the Earth's orbit can be estimated using the lengths of time between solstices and equinoxes. This analysis takes advantage of the fact that the eccentricity is small in order to greatly simplify the calculation.

#### BOOK REVIEWS

The Shock of Recognition: Motifs of Modern Art and Science by Lewis Pyenson by Raymond L. Lee, Jr., Reviewer

#### Additional Resources