Integral theorems such as Stokes’ and Gauss’ are fundamental in many parts of physics. For instance, Faraday’s law allows computing the induced electric current on a closed circuit in terms of the variation of the flux of a magnetic field across the surface spanned by the circuit. The key pointfor applying Stokes’ theorem is that this surface must be orientable. Many students wonder what happens to

Traditional stilts have been known in many countries in Asia and Africa and are generally used as toys. The designis very simple, but their use is very difficult. Performers have to train intensively to control their stability so they can walk using them. An interesting challenge is what kind of physical formulation controls the stability of traditional stilts. In this paper, we report a simple physical

When one object collides with another, the collision results in a loss of kinetic energy. The energy loss occurs mainly in the small volume of material that is compressed in the vicinity of the contact point. The effect was examined using a billiard cue with different tips. The resulting ball speed was found to vary strongly with the type of tip used, indicating that a large fraction of the energy

We discuss common student difficulties with the first and second laws of thermodynamics found using a validated conceptual multiple-choice survey called the survey of thermodynamic processes and first and second laws suitable for introductory physics courses. The analysis of data from more than a thousand students using the validated survey at six different colleges in the US shows that not only introductory

Mirrors that are convex in some places and concave in others can generate images of extended objects (such as the viewer’s face) that are curiously distorted and often topologically disrupted. Understanding these images involves the caustics of the family of rays emitted by each point of the object, and the totality of all such families constituting the rays from all points of the object. The general

In this work we show that the simplest results of the time independent perturbation theory (TIPT) can be used for the systematization of many experimental data from Atomic Physics. In particular, we will see applications to alkaline metals and different types of isoelectronic sequences, comparing the experimental data stored in the databases with simple parametrizations arising from the TIPT.

Motivated by the comment on our paper (2021 Eur. J. Phys. 42 045205) made by Ferreira D R, we carry out a comprehensive numerical comparison of the three known analytic expressions for the electrostatic potential of a uniformly charged triangle sheet. We report that the three expressions are equivalent to one another.

In a recent paper (2021 Eur. J. Phys. 42 045205), Kim etal carry out an analytical effort to arrive at an expression for the electrostatic potential due to a uniformly charged triangle. This appears to have been attempted by other authors before, with similar, but not exactly equal, numerical results. In addition, the paper leaves some doubts with regard to the comparison of the analytical expressions

Movement of air over a hole or cavity typically generates sound, which can have both noisy and tonal components (cavity noise, cavity tones). Such acoustic phenomena often tend to be a nuisance, e.g. for ‘buffeting’ or ‘wind throbbing’ noise, where airflow over an open side window or sunroof in a moving vehicle can produce low-frequency, high-amplitude ‘booming’ sound signals. The present contribution

An algorithm and spreadsheet for determining the energy states of a one-dimensional stepped rectangular-type well potential with infinite sides is described. The method is such that every student in a class could be assigned a unique homework problem which can be checked quickly by an instructor equipped with the generic spreadsheet described herein.

Solving physics problems is often done superficially, without making an in-depth analysis of the results obtained, limiting itself only to determining the numerical values of some physical quantities. In order to analyze the results obtained after solving physics problems and to more deeply understand the essence of the phenomena that take place, a graphic representation of the obtained results is

In this work, we follow the Green’s functions technique used by Atkinson and Crater (1975 Am. J. Phys. 43 301–304) to construct a solution of the one-dimensional Schrdinger equation with the delta derivative potential λδ′(x), λ being the coupling constant. The bound and the scattering states solutions were built using the complete set of eigenfunctions of the problem without the delta derivative potential

In this paper we look at the history and development of the so-called Lissajous figures. We show how to obtain the graphical representation of Lissajous figures in two and three dimensions, using Mathematica software. We show some of these figures, and the reader can modify the code to obtain any other figure. We also show how to build a simulation that shows the figure as a trajectory of a particle

String theory’s holographic QCD duality makes predictions for hadron physics by building models that live in five-dimensional (5D) curved space. We show that finding the hadron mass spectrum in these models amounts to finding the eigenvalues of a one-dimensional differential equation identical in form to the Schrdinger equation. Changing the structure of the 5D curved space is equivalent to altering

A general expression for the mean value of the sth power of the electron–nucleus separation for the (n, ℓ) state of the hydrogen atom is developed. The power s need not be an integer, and is restricted only to satisfying s > −2ℓ − 3.

We consider physical consequences, resulting from Coulomb’s and Ohm’s laws for the case of an anisotropic medium. First, we derive and analyze the expression for Coulomb’s force in the case of uniaxial crystals. We find that this force is a non-central force. At certain conditions its absolute value depends non-monotonically on the direction in the crystal. We also obtain the relation for the transverse

We present a simple experimental technique in which measurements of the changes in the mass of a sample volatile liquid are used to explore the relationship between the most probable energy and the environment temperature. We obtain the order of magnitude of the Boltzmann constant of gases.

Starting from a brief review on the concepts of electrical resistance and impedance and the definition of thermal resistance, it is shown how thermal impedance can be defined from a simple situation of an ideal semi-infinite solid sample subjected to uniform sinusoidal heating at its surface. Using the thermal impedance definition, the non-stationary component of the temperature field perpendicular

We designed a physics teaching lab experience for blind students to measure the wavelength of standing waves on a string. Our adaptation consisted of modifying the determination of the wavelength of the standing wave, which is usually done by visual inspection of the nodes and antinodes, using the sound volume generated by a guitar pickup at different points along the string. This allows one of the

In geophysics, wave propagation in elastic media is a crucial subject. In this context, seismology has made significant progress as a result of numerous advances, among these stands out the advancement of numerical methods such as the finite-difference one. Usually, seismic wave propagation in elastic media results in complex systems of partial differential equations, whose solutions cannot be obtained

Magnetic material is characterized by its magnetization that indicates the level to which it is magnetized. In this paper, a simple and inexpensive experiment is presented for determining the magnetization of a permanent magnet. It consists of investigating the vertical equilibrium position of a mobile system equipped with a NdFeB magnet as a function of its total mass, and an external magnetic field

In this report, we discuss the dynamics of photons in a five-dimensional Schwarzschild black hole. We find that the corresponding Eddington–Finkelstein-like coordinate admits two time-coordinate singularities for a particular condition. This condition is due to the existence of a non-zero angular momentum related to the extra spatial dimension. By introducing a new Regge–Wheeler tortoise coordinate

The paper explores the Rutherford scattering shadow in an entire class of comoving frames—inertial frames moving along the initial projectile direction—of which the laboratory frame, where the target is initially at rest, is a representative example. The paper is a continuation of the previous work addressing the scattering shadow in the fixed-target and the center-of-mass frame. It is shown that the

Inspired by Shulman’s question ‘where do teachers’ explanations come from?’, this study explores two issues: the extent to which student teachers (STs) of physics can detect consequential gaps in a given explanation (RQ1), and the extent to which they will sacrifice simplicity for completeness when designing an explanation for a given audience (RQ2). The chosen topic was the rainbow; focussing on the

Liquid properties are relevant for the understanding of fundamental and applied sciences. Among these properties, those that can be traced back and explained through the surface tension are particularly interesting to study and reconstruct in educational terms. Traditional educational treatment of surface tension is often obscure or too complex, sometimes superficial or completely neglected. The aim

The experiment with images described here contributes to the scarce literature about the experimental approach to the classical problem of oblique launching on the surface of an inclined plane. It is directed at an intermediate physics course, with the aim of contextualizing the teaching of the laws of friction and empirical modeling in Classical Mechanics. We used a video of a two-dimensional real

A covariant four-tensor rotation equation—for bi-dimensional composite body—, by generalising cross product to four-vectors, is obtained. From it, a relativistic angular impulse-angular momentum variation equation (Poinsot–Euler rotation equation) and its pseudo-work-rotational kinetic energy variation equation (Poinsot–Euler pseudo-work equation), are obtained for a body spinning—with constant angular

Ultrasound imaging, one of the most widely used diagnostic modalities, anchors the fields of medicine, physics, and engineering. In university classrooms, however, ultrasound imaging is often taught passively with a lack of practical element as the clinical machines are not easily available and there are very few alternative teaching tools available on the market. As part of an undergraduate student

When we watch a flying kite with a long tail hanging beneath, the tail sometimes oscillates and sometimes maintains a static shape. Generally, the tail portion deviates more when moving toward the free (bottom) end. The shape of the tail is described by a zeroth-order Bessel function where the coordinate origin locates at the tail’s bottom. In this paper, we derive simple equations to qualitatively

In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used in quantum field theory (QFT) where the bare values of the parameters of the theory run when an interaction is added. In this paper, we review some of these techniques

Experts know that bound state energy eigenvalues of a potential well are poles of its transmission amplitude, t(E). The textbooks do well by solving the bound states and scattering states separately, but the connection goes unheeded. Here, we present interesting and instructive illustrations, where we extract bound state eigenvalues from the known transmission coefficients (T(E) = |t(E)|2) for six

We present an in depth analysis and a new derivation of the Doppler factor in the Linard–Wiechert (LW) potentials, based on geometrical considerations in Minkowski space. We argue that, contrary to a common assumption, the methods used for deriving the Doppler factor in the case of an electrically charged extended particle are not applicable in the case of a point particle. A geometrical interpretation

In this paper, a qualitative explanation of the causes of surface tension forces at a liquid–gas interface acting parallel to an interface is presented. None of the common explanations of surface tension given in preliminary physics courses consider the reasons behind the attractive forces between nearest neighbor molecules acting parallel to a surface. The earlier proposed explanations are based on

We derive a general formula for the inertia tensor of a rigid body consisting of three particles with which students can learn basic properties of the inertia tensor without calculus. The inertia-tensor operator is constructed by employing the Dirac’s bra-ket notation to obtain the inertia tensor in an arbitrary frame of reference covariantly. The principal axes and moments of inertia are computed

If an egg rolls end over end along a horizontal surface, its centre of mass rises and falls. Four different rolling modes are described, namely pendulum oscillations, falling from rest, rolling without slipping and jumping in the air. Supplementary videos are provided for each type of motion, together with a theoretical analysis. The results in each case depend on the initial conditions and the coefficient

Mathematical and physical aspects in the analysis of pendulum motion in the presence of quadratic and linear damping are presented. New results are obtained from the analysis which are of research and educational interest. Closed-form expressions for the velocity vs large angle of swing are derived in the case of quadratic damping for both forward and backward swings. In the case of linear damping

A Timoshenko oscillator consists of an object set into motion through two opposite frictions of its rotating cylindrical supports. Coulomb’s law of friction determines that the oscillator’s motion should be simple harmonic vibration. However, experiments show that it is more like a damped vibration which is caused by non-Coulomb effects between the oscillator and two cylinders. We carefully measured

The textbook description of multiple slit interference employs a standard path difference formula that was originally calculated for the purpose of analyzing Young’s double slit experiment. It was arrived at on the basis of a pair of assumptions that help simplify the geometry of the slit-barrier-screen arrangement and the ensuing formalism needed to estimate the positions of interference fringes on

An interference of two beams coming from one laser is a well-known and popular experiment. But is it possible to obtain interference fringes using two completely independent laser sources? If the answer is ‘yes’, is such an observation available in a typical optical laboratory? We show a simple but spectacular method of observing such an interference, using very common continuous wave He–Ne lasers

We present an elegant derivation of the Doppler factor in the Linard–Wiechert potentials of an extended particle, based on a theorem authored by Synge and dealing with cross-sections through worldtubes.

We present an engaging levitation experiment that students can perform at home or in a simple laboratory using everyday objects. A cork, modified to be slightly denser than water, is placed in a jug containing tap water and coarse kitchen salt delivered at the bottom without stirring. The salt gradually diffuses and determines a stable density stratification of water, the bottom layers being denser

A looping pendulum is a setup that consists of two loads connected by a light string, which in turn is put over a fixed rod, with the lighter load being held by a person, and the heavier close to the rod. When the lighter load is released, experience shows there is an instant when the heavier load stops falling, and the lighter winds around the rod, bringing the system to rest. This setup is used in

Using basic concepts of cross sections, mean free paths for neutron travel, reproduction constants, and an expression for estimating the critical size of a self-sustaining nuclear chain reaction, it is possible to understand the dimensions of Enrico Fermi’s CP-1 nuclear pile. This development is suitable for undergraduate students, can be covered in one or two class periods, and can serve as a source

In this short paper we clarify and answer some issues addressed by Fernandez in his comment paper. Firstly, regarding the citation issue and secondly the technical issue regarding the analytical result of the quantum anharmonic oscillator with a delta potential.

High school physics teachers have a difficult job to do. On the one hand, they are charged with contributing to the creation of a scientifically literate society, while on the other they play a pivotal role in the recruitment of future physicists. Given the importance of this dual role, one might expect that the training of future physics teachers would be a priority for any physics department. However

The fundamentals of a quasi-relativistic wave equation, whose solutions match the Schrdinger results for slow-moving particles but are also valid when the particle moves at relativistic speeds, are discussed. This quasi-relativistic wave equation is then used for examining some interesting quantum problems where the introduction of relativistic considerations may produce remarkable consequences. We

Conics are relevant in many undergraduate course on classical physics, from free fall to Rutherford scattering. A pedagogical derivation of the intrinsic expressions of the curvature radius of different types of conic sections is presented. Our proof is carried out without resorting to any coordinate systems, but rather on using only elementary kinematic concepts together with basics of vector calculus

The nonlinear dynamics of a system of a compound double pendulum are experimentally analyzed and numerically verified. The experiments are carried out for a combination of initial angles in the range 0 ⩽ θ 0, ϕ 0 ⩽ 180, with zero initial angular velocity and with an increment of 1. The motion of the pendula is captured in the video and the individual pendula are tracked using image processing. The

The envelope of the orbits of particles released with the same speed but in different directions from a point in an attractive or repulsive Coulomb field is studied with a simple geometric approach. The lawn sprinkler problem and the shadow of the repulsive Rutherford scattering are considered as the limiting cases.

Spheres at medium interfaces are encountered in many applications, including in atomic force microscopy or indentation tests. Although the Hertz theory describes the contact mechanics between an elastic sphere and an elastic half-space for static loading and small deformations very well, there is a need to consider the density of the medium, the mass of the sphere and the radiation damping for dynamic

If a rod is held almost vertically with one end at rest on a horizontal surface then it will fall to the surface when released. The rod might pivot about its bottom end or it might slide forwards or backwards on the surface, depending on the coefficient of friction. Experimental and theoretical results are presented for a rod with a spherical bottom end. In that case the rod rolls on its bottom end

We analyze a recent discussion of one-dimensional quantum-mechanical models with a perturbation produced by a delta-function potential. We show that the authors failed to derive a correct transcendental equation for the eigenvalues in the case of the Morse oscillator because they omitted the contribution of the continuum spectrum in the basis set.

A new method to calculate the electric field inside a spherical shell with surface charge σ = σ o  cos θ in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical problem. For a flat surface of uniform charge density, the electric field normal to the surface is shown to be proportional to the solid angle subtended

Resistor networks are practical electric circuits and provide meaningful models to represent natural or artificial conductive structures. They can also be used to demonstrate how, in physics, general properties can be derived elegantly by combining general principles with symmetry properties. Here, this typical approach of physics is illustrated in the case of two-point resistances in the 2 n globe

A general Matlab program is designed to simulate the Fraunhofer diffraction patterns of a vortex beam through any apertures, which are usually used to compare with the experimental results in detecting the topological charge of a vortex beam. Two significant matrices are suggested in the above program: one related to the aperture, the other concerned with the field of vortex beam. Using the fast Fourier

With a pedagogical aim suited for the upper-division undergraduate, we apply the old quantum theory (pre-Schrdinger) to the study of many-electron atomic species. We eschew the typical picture with circular atomic Bohr orbits of non-zero angular momentum and instead consider the electrons to be ‘bouncing’ along straight lines on the nucleus. Abandoning the circular orbits of Bohr comes at the cost

In this paper we explore the analogies between optical physics and quantum mechanics. The formal similarity between the Helmholtz wave equation and the time-independent Schrdinger equation is presented. Details of the analogy between plane interface and potential step and between thin film and potential barrier are developed and a detailed discussion is provided to reinforce the analogy. We hope that

The dynamics of water micro-particles in air can be studied by introducing a viscous force in the equations of the motion, in addition to the weight of the particle and the buoyance force. In this work, by taking account of the buoyance force, the range of the micro-particle is calculated as a function of the angle at which it is released. An analytic-numerical procedure to find the angle giving the

This paper presents a didactic treatment of the rigid diatomic molecule under the action of an external electric field. We discuss the role of a new constant of motion that is valid when the electric field breaks spherical symmetry. We obtain the wave functions and the energies in the radial direction as well as the angular degrees of freedom, the latter corresponding to the eigenvalue spectrum of

Naked-eye observations of visible spectra using a transmission-grating-based spectrometer, with the spectral resolution of 0.2nm @ 550nm, are reported in this article. The resultant accuracy of the wavelength readout with the naked-eye is better than 1nm. The diffraction angles are precisely confirmed when the virtual diffraction image of the entrance slit (line spectrum) are collinear with two collimating