The question of the sources of electric and magnetic fields and their causes has been discussed extensively in the literature over the last decades. In this article, we approach this problem from the unified treatment of electromagnetic fields emphasizing the role of their sources in accordance with the cause-effect relationships. First, we…

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…

Quantum science is in the news daily and engages students' interest and curiosity. A fundamental quantum science concept that underpins medical imaging, quantum computing and many future technologies is quantum spin. Quantum spin can explain many physical phenomena that are in the lower secondary school curriculum, such as magnetism and light,…

We investigate learning difficulties among second-year students in electromagnetism courses when they apply Ampère-Maxwell's law. Using phenomenography, we analyzed written answers from 65 undergraduate physics students to four questions on Ampère's and Ampère-Maxwell's laws. We complemented our research by interviewing 12 students. To design the…

Electrostatic force is the preliminary and fundamental topic that forms the bedrock on which the conceptual framework of "electromagnetism" is built. Being a 'vector' quantity, electromagnetic force naturally inherits direction as well as magnitude. The conceptualization of such physical quantities may pose a challenge. The present work…

This work provides a missing manual needed to understand permanent magnets (also known as "hard" magnets), the only source of "magnetic induction field B" (units of teslas), often called the magnetic field, that students are familiar with when they confront magnetic force acting on moving charges. Students see this magnetic…

The question of whether Faraday's flux law is universal or whether there are exceptions has long been controversial. This discussion seemed to have recently concluded in favor of the generality of Faraday's Flux Law. The present article raises this question again with the aid of some rather simple measurements carried out on a Faraday generator.…

Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when describing real fields such as magnetic and electric fields, as the vector arrows can overlap. The present study…

We conducted a study with introductory and upper-division physics students in a Mexican university to learn how students independently recognize the electric field's main characteristics in the electric field lines diagram and as a source or target representation in conversion processes. We used the theory of registers of semiotic representations…

The question of how the processes around the Faraday generator with its rotating magnet should be interpreted has been controversial since its discovery by Faraday. Does the magnetic field rotate together with the rotating magnet or does it remain stationary? Furthermore, does one only need Faraday's flux law to interpret inductive processes, or…

A smartphone magnetometer is used to record the magnetic field of a freely falling point dipole magnet. The recorded magnetic field vs. time data are analyzed in accordance with the spatial dependence of the magnetic field to calculate the acceleration due to gravity g. The experiment gives local g to be 9.79 ± 1.9% m/s[superscript 2].

This paper reports on topic-specific pedagogical content knowledge (PCK) enacted by three pre-service science teachers during their final year school-based internship. An interpretive, qualitative case study was conducted to investigate to what extent the pre-service teachers applied the knowledge taught during a preceding physical science method…

In physics lessons at secondary school and experimental physics courses at universities, the magnetic field inside a current-carrying solenoid is considered quantitatively. The corresponding equations and theories are supported by measuring the magnetic flux density inside the solenoid with a Hall probe. It has already been shown that smartphones…

What colors do you use in class when teaching electromagnetism? For many physics educators we simply use what we learned or what is used in the textbook. Browsing through a large collection of introductory physics textbooks reveals that the vast majority use red for the electric field, blue for the magnetic field, and some shade of green for the…

One may be perplexed about the voltage across an inductor, since sometimes it is -LdI/dt, but more commonly it is LdI/dt. We explain why this is so, and point out that in fact, each of them is fine to be used if under its own sign convention (listed in table 2 in the last section of this paper), and the latter, mostly used in circuit equations, is…