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Equilibrium charge density on a thin curved wire
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| Pengarang | : | M. Shabri Abd. Majid,Rosylin Mohd. Yusof,David J. Griffiths |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1173-1182 |
| Abstrak | : | We address the electrostatic problem of a thin, curved, and cylindrical conductor (a conducting filament) and show that the corresponding linear charge density slowly tends to uniformity as the inverse of the logarithm of a characteristic parameter, which is the ratio of the diameter to the smaller of the length and minimum radius of curvature of the filament. An alternative derivation of this result based on energy minimization is given. These results follow from a general asymptotic analysis of the electric field components and potential near a charged filament in the limit of vanishing diameter. It is found that the divergent parts of the radial and azimuthal electric field components are determined by the local charge density, while the axial component is determined by the local dipole density. For a straight filament our results reduce to those known for conducting needles. For curved filaments, the configuration of charges and fields is no longer azimuthally symmetric, and there is an additional length scale arising from the finite radius of curvature of the filament. The basic uniformity result survives the added complications, which include an azimuthal variation in the surface charge density of the filament. As with the variations in linear charge density along the filament, the azimuthal variations vanish with the characteristic parameter, only more rapidly. These findings allow us to derive an asymptotic formula for the capacitance of a curved filament that generalizes a result first obtained by Maxwell. The examples of a straight filament with uniform and linearly varying charge densities and a circular filament with a uniform charge distribution are treated analytically and found to agree with the general analysis. Numerical calculations illustrating the slow convergence of linear charge distribution to uniformity for an elliptical filament are presented. An interactive computer program implementing and animating the numerical calculations is available. |
Those wonderful elastic waves
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1162-1172 |
| Abstrak | : | We consider elastic waves in isotropic and anisotropic media and discuss their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. The waves are represented by a wave function. For isotropic media this representation greatly simplifies the theory. The reflection of quasitransverse waves in anisotropic media from a free surface is shown to be characterized by three critical angles. |
Time series analysis with the Hilbert–Huang transform
| Pengarang | : | Edwin Rogers |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1154–1161 |
| Abstrak | : | Time series data can be transformed to the frequency domain via the Hilbert–Huang transform. This transform has two major stages. The data are first deconstructed into a set of monocomponent intrinsic mode functions that are the basis states for the transform. A Hilbert spectral analysis is then performed on each of these basis states, yielding time dependent amplitude and frequency information. The process of extracting the intrinsic mode functions and performing Hilbert spectral analysis is described and applied to a set of examples that show the advantages and shortcomings of this transform. |
First-order partial differential equations in classical dynamics
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1147-1153 |
| Abstrak | : | Carathèodory’s classic work on the calculus of variations explores in depth the connection between ordinary differential equations and first-order partial differential equations. The second-order ordinary differential equations of a classical dynamical system reduce to a single first-order differential equation in independent variables. The general solution of first-order partial differential equations touches on many concepts central to graduate-level courses in analytical dynamics including the Hamiltonian, Lagrange and Poisson brackets, and the Hamilton–Jacobi equation. For all but the simplest dynamical systems the solution requires one or more of these techniques. Three elementary dynamical problems (uniform acceleration, harmonic motion, and cyclotron motion) can be solved directly from the appropriate first-order partial differential equation without the use of advanced methods. The process offers an unusual perspective on classical dynamics, which is readily accessible to intermediate students who are not yet fully conversant with advanced approaches. |
Rotational states of a benzenelike ring and Bloch’s theorem
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1144-1146 |
| Abstrak | : | The rotational states and their energies for a model of a ringlike molecule are studied. It is found that the discrete cylindrical symmetry of the molecule gives rise to a new quantum number in addition to that for the usual quantized angular momentum ?. This new quantum number is formally analogous to but differs physically from the Bloch wave number for a one-dimensional crystal. The rotational states and energies of this model are discussed. |
Interference with polarized light beams: Generation of spatially varying polarization
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1135-1143 |
| Abstrak | : | We propose a method based on a Mach–Zehnder interferometer to analyze the superposition of polarized laser beams at a given angle. The focus of our study is the spatially varying polarization state of the resulting field, also known as a polarization grating, generated by this setup. Our proposal combines a description of the resulting field in terms of its Stokes parameters with an experimental demonstration of the existence of such a polarization grating due to the effects of polarization on beam interference experiments. |
Raman scattering of carbon disulfide: The temperature effect
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1130–1134 |
| Abstrak | : | A low-cost Raman system was constructed and used to perform Raman scattering measurements on liquid carbon disulfide at different sample temperatures. The and bands are identified based on the frequencies calculated by the normal mode analysis. The ratio of the intensities of the anti-Stokes and Stokes bands can be used to illustrate the Boltzmann distribution of the molecules among the vibrational energy levels. |
Spreadsheet physics: Examples in meteorology and planetary science
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1124-1129 |
| Abstrak | : | By utilizing the iterative capabilities of spreadsheets, students who do not have a programming background may obtain numerical solutions to complex equations. This paper discusses two examples of spreadsheet programming. One models the structure of a planet using a set of ordinary differential equations depending on the radius of the planet. The other involves coupled partial differential equations in a model of a planetary atmosphere. The results of the planetary models are compared to the values for Earth and Neptune. The results of the atmospheric model are compared to values for Earth’s atmosphere. |
Learning of content knowledge and development of scientific reasoning ability: A cross culture comparison
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1118–1123 |
| Abstrak | : | We report the results of our study of the connections between students’ learning of physics content knowledge and the development of general scientific reasoning abilities. In particular, we seek to determine whether and to what extent content learning affects the development of general reasoning abilities. Pre-college-instruction data of first-year college students in the United States and China were collected using the FCI, BEMA, and Lawson’s classroom test of scientific reasoning. We find that the rigorous learning of physics knowledge in middle and high schools has made a significant impact on the ability of students in China to solve physics problems, but this knowledge does not seem to have a direct effect on their general scientific reasoning ability, which is determined to be at the same level as that of the students in the United States. |
A student’s guide to searching the literature using online databases
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 77 (No. 12) |
| Halaman | : | 1112-1117 |
| Abstrak | : | A method is described to empower students to efficiently perform general and specific literature searches using online resources. The method was tested on undergraduate and graduate students with varying backgrounds in scientific literature. Students involved in this study showed marked improvement in their awareness of how and where to find accurate scientific information. |