The purpose of this article is to give the intelligible procedure for undergraduate students to grasp proof of the fact that the magnetic field outside the hollow superconducting sphere (superconducting shell) coincides with the field of a point magnetic dipole both when an uniform external magnetic field is applied as when a ferromagnetic sphere…

Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…

As part of a biomechanics course aimed at both upper-division Biology and Physics majors, this laboratory exercise introduces students to the ingenious ways in which organisms vary the composition and form of support and defensive structures such as bone and shell to maximize their strength while minimizing the energetic cost needed to produce…

An industrial-type distillation column, including appropriate pumps, heat exchangers, and automation, was used as a unit operations experiment to provide a link between classroom teaching and real-world applications. Students were presented with an open-ended experiment where they defined the testing parameters to solve a generalized problem. The…

The initial interaction among student, instructor, and content on the first day of class is critical in setting the stage for the remainder of the semester. While many students would like to ease into the semester, experienced faculty realize that the first day of class provides a one-time opportunity to shape the students' first impression…

Variations in the isotopic composition of elements have been widely used to study earth's climate, biosphere, and interior, and more recently to track the fate of contaminants. Within the broad range of elements that exhibit measureable isotopic variations, metal stable isotopes are increasingly applied across the biological, geological,…

While I was co-teaching an introductory course in musical acoustics a few years ago, our class investigated several pieces of equipment designed for audio purposes. One piece of such equipment was a pair of noise-canceling headphones. Our students were curious as to how these devices were in eliminating background noise and whether they indeed…

At Appalachian State University students have to take just two semesters of a physical or biological science to satisfy the general education requirements. Most non-science major students have little time in their crowded schedules to take additional science courses, whether they want to or not, and in fact face a surcharge when taking more…

I have used many ploys to start a course in introductory physics, but one of the more interesting ones was to spend 20 minutes describing some of the curves and shapes that we would encounter in our year together. The students saw parabolas, catenaries, hyperbolas, cycloids, circles, ellipses, and helices, and were shown examples, either live or…

This study introduces a new group of students to the postsecondary science agenda: "latecomers to science." Latecomers, who enter postsecondary science through alternative routes because they are missing prerequisites, are less likely to graduate than traditional science students. Challenges to latecomers' persistence are explored…

In a recent article by the authors, the suggestion was made that arrow pushing, a widely used tool in organic chemistry, could also be profitably employed in the teaching of introductory inorganic chemistry. A number of relatively simple reactions were used to illustrate this thesis, raising the question whether the same approach might rationalize…

Nearly 100 years ago de Donder introduced the term "extent of reaction", ?. We build on that work by defining the concept of reagent extrema for an arbitrary chemical reaction, aA + bB [reversible reaction] yY + zZ. The central equation is ?^[subscript i] = -n[subscript i,0]/?[subscript i]. The symbol ?^[subscript i] represents the…

Throughout the centuries, the concept of "element" has undergone a clear evolution from a strictly philosophical area to the scientific domain, although the conceptual progress has not always gone along with a terminological evolution. Some inconsistencies in the definition of element can be found in several precollege and…

Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions…

In a previous paper that focused on the transmission of periodic waves at the boundary between two media, we documented difficulties with the basic concepts of wavelength, frequency, and propagation speed, and with the relationship v=f[lambda]. In this paper, we report on student attempts to apply this relationship in problems involving two-source…