Related papers: Upper-division Student Understanding of Coulomb's …
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
Helping students learn why Gauss' law can or cannot be easily applied to determine the strength of the electric field at various points for a particular charge distribution, and then helping them learn to determine the shape of the Gaussian…
The Coulomb problem for continuous charge distributions is a central problem in physics. Powerful methods, that scale linearly with system size and that allow us to use different resolutions in different regions of space are therefore…
We have been investigating the difficulties that students in upper-level undergraduate courses have in determining the probability distribution for measuring energy and position as a function of time when the initial wave function is…
We investigate upper-division student difficulties with direct integration in multiple contexts involving the calculation of a potential from a continuous distribution (e.g., mass, charge, or current). Integration is a tool that has been…
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often…
We present a theoretical approach to study the dynamics of spherical, cylindrical and ellipsoidal charge distributions under their self-Coulomb field and a stochastic force due to collisions and random motions of charged particles. The…
We investigate learning difficulties among second-year students on electromagnetism courses when they apply Amp\`ere-Maxwell's law. Using phenomenography, we analysed written answers from 65 undergraduate physics students to four questions…
We investigate the difficulties that students in calculus-based introductory physics courses have with the concepts of symmetry, electric field, and electric flux which are important for applying Gauss's law. The determination of the…
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
Prior research suggest that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for…
The Dirac delta function is a standard mathematical tool used in multiple topical areas in the undergraduate physics curriculum. While Dirac delta functions are usually introduced in order to simplify a problem mathematically, students…
Standardized assessment tests that allow researchers to compare the performance of students under various curricula are highly desirable. There are several research-based conceptual tests that serve as instruments to assess and identify…
We discuss the development and evaluation of five research-based tutorials on Coulomb's law, superposition, symmetry and Gauss's Law to help students in the calculus-based introductory physics courses learn these concepts. We discuss the…
Electromagnetism (E&M) is often challenging for students enrolled in introductory college-level physics courses. Compared to mechanics, the mathematics of E&M is more sophisticated and the representations are more abstract. Furthermore,…
The concept of potential difference is fundamental to understanding electricity in upper secondary physics courses. However, students often find it challenging to grasp. To address this, we designed and implemented a test aimed at assessing…
The Coulomb gap in a donor-acceptor model with finite charge transfer energy $\Delta$ describing the electronic system on the dielectric side of the metal-insulator transition is investigated by means of computer simulations on two- and…
We investigated the difficulties that physics students in upper-level undergraduate quantum mechanics and graduate students after quantum and statistical mechanics core courses have with the Fermi energy, the Fermi-Dirac distribution and…
The objective of this introduction to Colombeau algebras of generalized-functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic non-linear…
We describe the potential produced by a point electric charge placed into a constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length. The standard Coulomb law is modified due to the vacuum…