It is difficult for an instructor to just make up valid numbers for B[subscript x], B[subscript y], B[subscript z], E[subscript x], E[subscript y], and E[subscript z] in the creation of homework problems and test questions calculating the Poynting vector. In this paper, 25 examples are given of the electric and magnetic fields of electromagnetic…

Electricity and magnetism are closely related phenomena with a well-known symmetry found in Maxwell equations. An essential part of any electricity and magnetism course includes the analysis of different field source distributions through Gauss's and Ampere's laws to compute and interpret different physical quantities, such as electric flux,…

Science and engineering students in the second semester of a calculus-based physics sequence typically study and measure the on-axis magnetic field for a multiple, circular turn coil. There are four benefits to this approach: 1) an analytical solution is easily obtained, 2) the coil is easily constructed using tightly wound, high-gauge wire where…

Interaction forces between magnetic fields and current loops play a central role in the theory of magnetism. This work describes a reasonably simple and cheap experiment for demonstrating this issue: the force on a thin coil due to a nearby cylindrical magnet. The magnitude of the force as well as its attractive/repulsive character is comfortably…

There have been a few methods described in this journal and elsewhere for measuring the wavelength of the standing electromagnetic waves in a microwave oven. Typically, these involve melting chocolate, cheese, or some other substance on a plate that is prevented from rotating. In this article I describe a more dynamic and colorful technique that…

It can readily be demonstrated that when a low frequency alternating voltage is applied to an iron-core coil the impedance is much higher than the direct current resistance of the coil. To understand how the high level of impedance arises it is necessary to explain how magnetic and electrical induction give rise to a current in the coil that…

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 historically studied at several different points in the curriculum including introductory and upper-division…

As science becomes increasingly computationally intensive, the need for computational thinking (CT) and computer science (CS) practices in K-12 science education is becoming paramount. Incorporation of CT/CS practices in K-12 education can be seen in national standards and a variety of allied initiatives. One way to build capacity around an…

Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector…

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

If we drop a magnet through a coil, an emf is induced in the coil according to Faraday's law of electromagnetic induction. Here, such an experiment is done using expEYES kit. The plot of emf versus time has a specific shape with two peaks. A theoretical analysis of this graph is discussed here for both short and long cylindrical magnets.…

There is no doubt that integrated concepts inspire students and take learning to a new level. As we fly, we fly through the magnetic field of the Earth. We used the concepts involved in flying to develop an exercise that bonds geology, physics and life sciences.

In undergraduate E&M courses the magnetic field due to a finite length, current-carrying wire can be calculated using the Biot-Savart law. However, to the author's knowledge, no textbook presents the calculation of this field using the Ampere-Maxwell law: ?B [multiplied by] dl = µ[subscript 0] (I + e[subscript 0] dF/dt) [multiplied by] 1

This study aims to develop a semiotic declarative knowledge model, which is a positive constructive behavior model that systematically facilitates understanding in order to ensure that learners think accurately and ask the right questions about a topic. The data used to develop the experimental model were obtained using four measurement tools…

A computational experiment investigating the [superscript 1]H and [superscript 13]C nuclear magnetic resonance (NMR) chemical shifts of molecules with unpaired electrons has been developed and implemented. This experiment is appropriate for an upper-level undergraduate laboratory course in computational, physical, or inorganic chemistry. The…