Vol. 20 No. 2 Jul-Dec (2023): Revista Mexicana de Física E

We review the Feynman paradox related to the conservation of the angular momentum in systems with an electromagnetic field. We show that the angular momentum is conserved if it is adequately defined.

Education today is required to utilize technological knowledge and skills in preparation for global competition. Along with the rapid development of technology, educators are required to develop learning alternatives. The purpose of this research is to create a particle trajectory simulation that is used as an alternative to online learning. The simulation uses Python programming language and Origin Pro assisted spreadsheet. Simulation in Python programming uses the Euler Cromer method to describe particle trajectories affected by electric and magnetic fields. This paper has successfully simulated particle trajectories affected by electric and magnetic fields with the Python programming language and Spreadsheet. The case where the motion of a charged particle is affected by a combination of electric and magnetic fields is when a positively charged particle moves perpendicular to the magnetic field, it will form a helical trajectory. However, when the electric field is in the direction of the magnetic field, the motion in the direction of the magnetic field will be accelerated by the electric force in the direction of the magnetic field which causes the helix to increase in width.

Max Planck (1858-1947) is one of the most renowned scientists in physics. He is even a commonplace character in humanities courses since he was one of the European scientists who most influenced the opinion and perspective of European society. This work intends to present a pedagogical introduction to the quantization of energy, Planck's most valuable contribution to science. This is an important topic that is frequently included in physics and engineering curricula but is often presented in a vague and forced manner. This work seeks a more intuitive introduction to the quantization of energy by presenting Planck's law and the Casimir force, along with a practical activity that students can perform to directly measure Planck's constant and achieve a more cohesive understanding of the concepts

Conservation theorems of Mechanics, have been applied to the problem consisting of a body rotating on a frictionless table, attached to a hanging body, as an illustrative example for students of Physics with no knowledge of sophisticated mathematical methods, how to obtain a description of the physical behavior of a system, when obtaining the equation of motion requires those complicated methods. Applying the conservation of angular momentum it is shown that the angular frequency increases inversely to the square of the radius of motion; then the radius  is found at which the centripetal force and the tension of the string compensate each other; then, applying the conservation of energy, turning points are found. At the end, following scenery is obtained: the radial component of motion of the rotating body takes place between two turning points, namely a maximum at  given by the initial conditions, and a minimum at . With the help of these equations, obtained without the need of solving differential equations, it is possible to obtain a semi quantitative physical behavior of this particular system.

The purpose of this research is to understand the physics education concepts through solving unit review problems in free fall topic. This research is a quantitative descriptive study involving 19 students of Physics Education at the University of Tamansiswa. The test instrument consists of 2 essay questions that refer to problem-solving indicators. The results of the study obtained several findings. Analysis of understanding the concepts of physics education students through solving unit review problems in free fall topic had the highest percentage in the medium category. On the problem solving indicators Physics Approach, Specific Application of Physics, and Logical Progression students’ abilities are in the low category.

The HHL quantum algorithm [1] is a procedure that addresses the resolution of linear systems of equations (QLSP). Under certain conditions, the algorithm has a logarithmic order in the number of equations, better than the faster classical method. The algorithm manages to find a quantum state proportional to the solution vector, up to a normalization factor. The disadvantage is that to determine each of the coefficients of the solution vector, the algorithm’s output quantum state must be determined with additional statistical methods, thus losing its exponential advantage. There are certain types of problems in which this disadvantage can be circumvented, the statistical treatment is unavoidable, but for certain cases such as electrical circuits, in which the main interest is to find only one of the currents, (for example the load current), we only need to measure one of the qubits of the solution state. In this article we solve the linear system associated with the currents of an electrical circuit with sinusoidal voltage, using the HHL algorithm, simulated in a Scilab numerical environment. An optimized example of an electrical line transmission wave in a real computer on the IBMQ platform, is also solved

The antecedent of this contribution is [1], which constructed the harmonic bidimensional expansions for the electrostatic and magnetostatic potentials, produced by a straight line with uniform charge and uniform current distributions, respectively, in Cartesian, and cylindrical circular, elliptic and parabolic coordinates. For the successive geometries, the sources are confined in the respective cylinders containing the source line, plus induced sources in two grounded flat, elliptical and parabolic plates; the potentials are continuous at the source cylinder and vanish at the grounded plates. In the electrostatic case, the electric intensity field is evaluated as the negative of the gradient of the potential; in the magnetostatic case, the magnetic induction field is the rotational of the axial potential. Both potential and force fields are bidimensional, and the equipotential surfaces and force fields are orthogonal. The normal components of the electric field at the source cylinder show a discontinuity, which according to Gauss’s law is a measure of the surface charge distribution; in contrast, the tangential components are continuous due to the conservative character of the electrostatic force. The normal components of the induction field are continuous due to its solenoidad character; its tangential components show a discontinuity which by Ampere’s law is a measure of the linear current intensity. Figures 1-4 illustrate the equipotentials on the left and electric field lines on the right; and the magnetic field lines on the left and the equipotentials on the right, exhibiting also their respective orthogonalities. The differences between the electric and magnetic multipoles are recognized, but we can still ask if there is a connection between them. The answer is given here in terms of the Lorentz transformations of the four-vector potentials and sources, and of the antisymmetric force field four-tensor.

En este manuscrito presentamos una aplicación web con soporte en lenguaje de programación PYTHON, REACTJS y JAVASCRIPT, libre y abierta, para el desarrollo de una actividad de enseñanza-aprendizaje de la astronomía, específicamente para el cálculo de la rotación diferencial del Sol para estudiantes y publicó en general en edad escolar entre 10 y 18 años. El propósito fundamental es la de difundir el conocimiento del Sol y algunas de sus propiedades. La aplicación web es autocontenida y con suficiente guía y ayuda para que cualquiera pueda usarla, además de su dinamismo y diseño innovador, pretende presentar estrategias agradables para la enseñanza y aprendizaje de la ciencia en torno al Sol.

In this manuscript we present a web application with support in PYTHON, REACTJS and JAVASCRIPT programming language, free and open, for the development of a teaching-learning activity of astronomy, specifically for the calculation of the differential rotation of the Sun for students and general public in school age between 10 and 18 years old. The main purpose is to spread the knowledge of the Sun and some of its properties. The web application is self-contained and with enough guidance and help for anyone to use it, in addition to its dynamism and innovative design, it aims to present pleasant strategies for teaching and learning science around the Sun.

This paper shows solutions of ordinary differential equations (EDOS) obtained by using two symbolic packages: Symbolic Math Toolbox™ (Matlab) and SymPy (Python). The basic instructions to obtain solutions of both packages are explained step by step, through a group of examples from a traditional ordinary differential equations course. Differential equations that are solved with methods such as: separable variables, linear equations, indeterminate coefficients, variation of parameters, power series, Laplace transform, and numerical solutions are included. By means of the symbolic computation carried out with these packages it is possible to obtain the solution of linear systems, as well as the visualization of the direction field of a differential equation or of a non-linear system of differential equations. The main contribution of this work consists in providing the reader with a practical guide that allows him to start the study of differential equations assisted by Symbolic Math Toolbox™ or SymPy. Among the benefits of using these computational tools in teaching and/or learning practices, it is shown how the use of symbolic or numerical computation saves us effort in the computation of tedious calculations; focusing attention on important ideas and concepts such as: the relationship between the mathematical model and its physical counterpart, asymptotic behavior and qualitative analysis of the solutions.

Chemical kinetics studies chemical reactions and their mechanisms. These kind of mechanisms are understood as a sequence of elementary steps to carry out the chemical reaction. In the present work, a Markov chain model is applied to the modeling of chemical reactions such as 1st- and 2nd-order reactions, competitive-parallel reactions, consecutive or serial reactions, and competitive-consecutive reactions. Additionally, a comparison of the Markov chain model with analytical and numerical solutions is included. In all cases, a good agreement is observed between the results.

La  cinética quı́mica estudia las reacciones quı́micas y sus mecanismos de reacción. Estos mecanismos se entienden como una secuencia de pasos elementales  para llevar a cabo la reacción química. En el presente trabajo se utiliza un modelo de cadenas de Markov aplicado al modelado de reacciones quı́micas tales como: reacciones de primer y segundo orden, reacciones competitivas-paralelas, reacciones consecutivas o en serie y reacciones competitivas-consecutivas. Adicionalmente, se incluye una comparación de las soluciones analı́ticas y numéricas de cada una de las reacciones de interés. En todos los casos se observa una buena concordancia entre los resultados empleando cadenas de Markov, la solución numérica y la solución analı́tica.

Students of physics, engineering and related majors; generally, do not know the usefulness and applications of transforming a signal from the time domain to the frequency domain. The mathematics that makes possible this transformation is well known to senior students of the majors, but vaguely applied in teaching laboratories. The main phenomena that could provide us with frequency information, the pendulum and the spring, are minimized by focusing only on obtaining the mathematics dictated in books.  The pendulum is the most studied physical system in teaching laboratories from precollege up to college levels; this phenomenon is analyzed mathematically in most of the related literature in the area of Physics and Engineering. It is an introduction to the wave phenomenon. However, teaching paradigms, focus on the plain demonstration that periods are invariant to suspended masses, if and only if the oscillation is within angles not greater than 10 degrees from their normal. The use of technologies, computational and electronic, also focuses on the demonstration of such assertion. In the present work, a mechanical-electrical system was designed that allows to observe, in real time, on the screen of an oscilloscope, the swinging behavior of a pendulum. This system makes evident that the swing movement of a pendulum can be described by a sine function, but also with this same system, and with the help of a digital oscilloscope, it is possible to simultaneously observe the signal generated in the temporal domain and in the frequency domain. This innovation not just breaks the paradigms of teaching but also promotes an alternative to valuable observations promotes understanding.

A mini review of attitudes and beliefs toward physics has been carried out. The purpose of this study was to address aspects that influence attitudes and beliefs toward physics and various learning models that can increase attitudes and beliefs toward physics. The method used in this study was literature review. Literature review was done by searching for keywords, i.e.: attitudes towards physics and beliefs towards physics. This keyword search was done through Google Scholar, Base, and Core search engines. We have obtained 25 articles that matched the keywords and have been screened with the limitation of the year of publication, namely the last 10 years. Through this literature review it can be obtained that physics attitudes and beliefs were influenced by gender and personality, grade level, type of school, and age. Contradictions regarding aspects that influence attitudes and beliefs about physics occur in the gender aspect. Various learning methods to improve attitudes and beliefs about physics were cooperative learning models with jigsaw, Science Technology Engineering and Mathematics (STEM), concept maps, peer instruction methods, open inquiry methods, learning integrated with music, and learning using a computer simulation model.

The examples usually solved by means of the method of images are revisited solving directly the Laplace equation. We also give a simple derivation of the axially symmetric solutions of the Laplace equation in spherical coordinates and of the translationally symmetric solutions of the Laplace equation in cylindrical coordinates.

We consider the Foldy-Whouthuysen (FW) transformation of the Dirac equation coupled to a background soliton field which is equivalent to a position-dependent massm(x) such that at each limit x → ±∞, the mass to the left and to the right tends to a (possibly different) constant, with a sign difference at each side. We then build-up a third order unitarily transformed Schrödinger-like Hamiltonian as a counterpart of the corresponding to the well known Jackiw-Rebbi model. By further FW-transforming the Dirac spinor, we establish the relation between the non-relativistic and relativistic wave functions up to this order of approximation for generic position dependent mass profiles. For the economic choice m(x) = m0x/|x|, we find that these spinors are the same up to an overall constant.