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Drag and lift forces between a rotating conductive sphere and a cylindrical magnet
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| Pengarang | : | Mark A. Nurge |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 6) |
| Halaman | : | 443-452 |
| Abstrak | : | Modeling the interaction between a non-uniform magnetic field and a rotating conductive object provides insight into the drag force, which is used in applications such as eddy current braking and linear induction motors, as well as the transition to a repulsive force, which is the basis for magnetic levitation systems. Here, we study the interaction between a non-uniform field generated by a cylindrical magnet and a rotating conductive sphere. Each eddy current in the sphere generates a magnetic field which in turn generates another eddy current, eventually feeding back on itself. A two-step mathematical process is developed to find a closed-form solution in terms of only three eddy currents. However, the complete solution requires decomposition of the magnetic field into a summation of spherical harmonics, making it more suitable for a graduate-level electromagnetism lecture or lab. Finally, the forces associated with these currents are calculated and then verified experimentally. |
Sympathetic resonance
| Pengarang | : | Lawrence N. Virgin |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 6) |
| Halaman | : | 439-442 |
| Abstrak | : | This short paper describes a useful teaching tool, ideal for demonstration purposes within the classroom or lab setting. It is based on the simple dynamic response of flexible cantilevers and evolves naturally from the underlying principles of a vibrating reed tachometer. Utilizing a 3D-printer, these ideas conveniently encompass the phenomenon of resonance in which all the cantilevers of a similar length respond in harmony when just one of their number is plucked. |
The metallic sphere in a uniform ac magnetic field: A simple and precise experiment for exploring eddy currents and non-destructive testing
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 6) |
| Halaman | : | 430-438 |
| Abstrak | : | We describe a very simple experiment that utilizes standard laboratory equipment to measure the electromagnetic response of a metallic sphere exposed to a uniform ac magnetic field. Measurements were made for a variety of non-magnetic and magnetic metals, and in all cases the results fit very well with theory over the four orders of frequency (25 Hz to 102 kHz) explored here. Precise values of magnetic permeability and electrical conductivity can be extracted from fits to the data given the sphere radius only. The same apparatus is also used to explore the effects of geometry on eddy current generation as well as to demonstrate non-destructive testing through measurements on coins of different composition. |
On Faraday's law in the presence of extended conductors
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 6) |
| Halaman | : | 422-429 |
| Abstrak | : | The use of Faraday's Law of induction for calculating the induced currents in an extended conducting body is discussed. In a general case with arbitrary geometry, the solution to the problem of a moving metal object in the presence of a magnetic field is difficult and implies solving Maxwell's equations in a time-dependent situation. In many cases, including cases with good conductors (but not superconductors) Ampère's Law can be neglected and a simpler solution based solely in Faraday's law can be obtained. The integral form of Faraday's Law along any loop in the conducting body is equivalent to a Kirkhhoff's voltage law of a circuit. Therefore, a numerical solution can be obtained by solving a linear system of equations corresponding to a discrete number of loops in the body. |
Theory and experiment on charging and discharging a capacitor through a reverse-biased diode
| Pengarang | : | Smith, P. Sean |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 6) |
| Halaman | : | 417-421 |
| Abstrak | : | The beauty of a diode lies in its voltage-dependent nonlinear resistance. The voltage on a charging and discharging capacitor through a reverse-biased diode is calculated from basic equations and is found to be in good agreement with experimental measurements. Instead of the exponential dependence of charging and discharging voltages with time for a resistor-capacitor circuit, a linear time dependence is found when the resistor is replaced by a reverse-biased diode. Thus, well controlled positive and negative ramp voltages are obtained from the charging and discharging diode-capacitor circuits. This experiment can readily be performed in an introductory physics and electronics laboratory. |
Quantum entanglement with Freedman's inequality
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 6) |
| Halaman | : | 412-416 |
| Abstrak | : | The assumption of local realism imposes constraints, such as Bell inequalities, on quantities obtained from measurements. In recent years, various tests of local realism have gained popularity in undergraduate laboratories, giving students the exciting opportunity to experimentally contradict this philosophical assumption. The standard test of the CHSH (Clauser–Horne–Shimony–Holt) Bell inequality requires 16 measurements, whereas a test of Freedman's inequality requires only three measurements. The calculations required to test Freedman's inequality are correspondingly simpler and the theory is less abstract. We suggest that students may benefit from testing Freedman's inequality before proceeding to the CHSH inequality and other more complicated experiments. Our measured data violated Freedman's inequality by more than six standard deviations. |
Diffraction effects in mechanically chopped laser pulses
| Pengarang | : | Samridhi Gambhir |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 6) |
| Halaman | : | 406-411 |
| Abstrak | : | A mechanical beam chopper consists of a rotating disc of regularly spaced wide slits which allow light to pass through them. A continuous light beam, after passing through the rotating disc, is switched-on and switched-off periodically, and a series of optical pulses are produced. The intensity of each pulse is expected to rise and fall smoothly with time. However, a careful study has revealed that the edges of mechanically chopped laser light pulses consist of periodic intensity undulations which can be detected with a photo detector. In this paper, it is shown that the intensity undulations in mechanically chopped laser pulses are produced by diffraction of light from the rotating disc, and a detailed explanation is given of the intensity undulations in mechanically chopped laser pulses. An experiment presented in this paper provides an efficient method to capture a one dimensional diffraction profile of light from a straight sharp-edge in the time domain. In addition, the experiment accurately measures wavelengths of three different laser beams from the undulations in mechanically chopped laser light pulses. |
An experimental demonstration of avoided crossings with masses on springs
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 7) |
| Halaman | : | 526-530 |
| Abstrak | : | We experimentally demonstrate an avoided crossing by coupling two harmonic oscillators. Each harmonic oscillator consists of a mass connected to a stationary wall by a spring. The two harmonic oscillators are coupled by a spring connecting the two masses. An avoided crossing is experimentally demonstrated in two ways: first, by adjusting the spring constant of one oscillator, and then by separately adjusting the mass of the oscillator. In both cases, the adjusted parameter is held constant for the second oscillator. Additionally, we examine the effects from altering the coupling between the two oscillators. These experimental results are shown to be consistent with theoretical predictions. |
An asymmetric isochronous pendulum
| Pengarang | : | Juan M. Randazzo |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 7) |
| Halaman | : | 518-525 |
| Abstrak | : | In this work, we propose a novel asymmetric isochronous pendulum, where half of the trajectory corresponds to that of the (non-isochronous) simple pendulum, while the remaining part corresponds to a specific trajectory. The pendulum's complete swing is isochronous—i.e., its period is not dependent on the oscillation amplitude. This new design is inspired by the symmetric isochronous Huygens pendulum, in which the trajectory is modified by cycloidal guides. In our case, only one guide is needed, for which analytical expressions are given for the first time. The objective of the paper is to add a new pedagogical tool in the undergraduate-level physics courses for understanding the isochronism concept, specifically the time delay for large amplitudes in the simple pendulum must be compensated by accelerating it along the new trajectory. We also introduce a novel numerical method to find the trajectory, based on the convergent superposition of straight trajectories (inclined-plane type) to approximate the curve. The procedure is not only accurate, but it is also appropriate for introducing the concepts of differential calculus and inclined-plane mechanics. |
A simple game simulating quantum measurements of qubits
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 7) |
| Halaman | : | 510-517 |
| Abstrak | : | Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics course to build intuition and quantitative understanding of the probabilistic nature of quantum measurements in two-level systems such as qubits or the Stern–Gerlach experiment. The goal of the game is to guess a quantum state secretly chosen from a given set in the fewest number of measurements. It uses 20-sided dice or other classical random number generators to simulate quantum measurements. The Bloch vector formalism is introduced to give a geometric description of the quantum states and measurement outcomes. Several ready-to-use sets of quantum states are given, so readers can jump right in and try the game themselves without any prior knowledge of quantum mechanics. More advanced students can also use the game in suggested follow-up exercises to deepen students' understanding of quantum measurements and their statistical description. |