Related papers: Teaching Magnetism with Bivectors
Throughout introductory physics, students create and interpret free body diagrams in which multiple forces act on an object, typically at a single location (the object's center of mass). The situation increases in difficulty when multiple…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is relatively form-bounded with respect to the real part of the…
Principal angles are used to define an angle bivector of subspaces, which fully describes their relative inclination. Its exponential is related to the Clifford geometric product of blades, gives rotors connecting subspaces via minimal…
This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler…
We discuss several similarities and differences between the concepts of electric and magnetic dipoles. We then consider the relation between the magnetic dipole and a current loop and show that in the limit of a pointlike circuit, their…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a…
In this paper the proofs are given that the electric and magnetic fields are properly defined vectors on the four-dimensional (4D) spacetime (the 4-vectors in the usual notation) and not the usual 3D fields. Furthermore, the proofs are…
We give a pedagogical introduction to two aspects of magnetic fields in the early universe. We first focus on how to formulate electrodynamics in curved space time, defining appropriate magnetic and electric fields and writing Maxwell…
Special Relativity is often seen as a conceptually difficult topic, which in turn is difficult to effectively teach. This work focuses on the role of visualizations as a tool in teaching Special Relativity at the secondary or university…
A thoughtless treatment of Maxwell's equations can lead to the interpretation of the existence of a causal relationship between their different terms and, therefore, that an electric field that varies in time generates a magnetic one and…
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the the…
A self-contained introduction is presented of the notion of the (abstract) differentiable manifold and its tangent vector fields. The way in which elementary topological ideas stimulated the passage from Euclidean (vector) spaces and linear…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
Light Polarization has many technological applications and its discovery was crucial to reveal the transverse nature of the electromagnetic waves. However, despite its fundamental and practical importance, in high school this property of…
Eigenvectors of stress-energy tensor (the source in Einstein's equations) form privileged bases in description of the corresponding space-times. When one or more of these vector fields are rotating (the property well determined in…
After a few historic remarks on magnetic materials we introduce the basic definitions related to permanent magnets. The magnetic properties of the most common materials are reviewed and the production processes are described. Measurement…
The development of Information and Communication Technologies suggests some spectacular changes in the methods used for teaching scientific subjects. Nowadays, the development of software and hardware makes it possible to simulate processes…