Search

An estimate of the dynamic effect the electric fields of a charged sphere on a current-carrying conductor is obtained. The characteristic time parameter of charge transfer to a conducting sphere, as well as the momentum Conservation Principle are applied. The found values of the interaction force and the transmitted energy can make it possible to determine the physical nature of the dynamic effect. A description of the laboratory setup is presented.

This article proposes the study of Ampere's Law, which is taught in the Physics course of undergraduate engineering courses in Brazil, using the hypothesis of the finite-length conductor instead of the infinite-length conductor. For this, it is necessary to use Stokes' Theorem, which in the case of infinite conductor is dispensed with. The feasibility of this proposal is supported by the fact that the techniques to calculate the line integrals and flux integrals, necessary in our proposal, are taught in the disciplines of Calculus. This approach allows a clear distinction between the "current enclosed" by the closed curve of the amperian line integral and the current actually flowing through the conductor. With the assumption of the infinite length conductor these two currents are indistinguishable. Another benefit of this approach is that the displacement current can be introduced intuitively as the flux integral of the curl of the magnetic field that appears in one of the members of the Stokes equation. [ABSTRACT FROM AUTHOR]

This paper presents the mechanism and potential advantages of flux pinned docking interface mainly composed of a high temperature superconductor and an electromagnet. In order to readily assess the connection characteristics of flux pinned docking interface, the force between a high temperature superconductor and an electromagnet needs to be investigated. Based on the magnetic dipole method and the Ampere law method, the force between two current coils can be compared, which shows that the Ampere law method has the higher calculated accuracy. Based on the improved frozen image model and the Ampere law method, the force between high temperature superconductor bulk and permanent magnet can be calculated, which is validated experimentally. Moreover, the force between high temperature superconductor and electromagnet applied to flux pinned docking interface is able to be predicted and analyzed. The connection stiffness between high temperature superconductor and permanent magnet can be calculated based on the improved frozen image model and Hooke's law. The relationship between the connection stiffness and field cooling height is analyzed. Furthermore, the connection stiffness of the flux pinned docking interface is predicted and optimized, and its effective working range is defined and analyzed in case of some different parameters. [ABSTRACT FROM AUTHOR]

In highly efficient power electronic systems, circular arrays of magnetic field sensors offer numerous advantages compared to older magnetic core-based sensors. They feature low power consumption, low weight, and high immunity to external magnetic fields. In power converters, conductors with a rectangular cross section, a small height, and a large width are widely used. Thus, an elliptical sensor array could reduce the space needed for the current sensor, e.g., in a power converter by a factor of four or more compared to a circular sensor array. In this work, we theoretically and experimentally study the sensitivity error caused by the change of the conductor geometry. Therefore, we calibrated different elliptical sensor arrays on a circular conductor and determined the sensitivity error for the use of flat conductors with different widths. This calibration on a circular conductor avoids a costly conductor-specific calibration of the sensor array in the application. Two different distribution methods for elliptical sensor arrays and different ratios of the semiaxes are considered. In addition, the influence of the number of sensors and the starting position for the sensors are examined. The presented elliptical sensor arrays can be used to measure the current carried by a flat conductor largely independent of its width. For some aspect ratios, they even offer a lower sensitivity error than circular sensor arrays. In this article, design considerations for those elliptic sensor arrays are given. [ABSTRACT FROM AUTHOR]

By the introduction of a generalized magnetic vector potential, which contains the contributions of both the magnetic and electric parts, and the use of the Ampere's law within the quasistatic approximation as the state equation, the partial differential equations for governing the electromagnetic properties of superconductors as well as the surrounding coolant were established and numerically discretized by resorting to the finite-element technique and finite-difference scheme, respectively, in the spatial and temporal domain. In conjunction with an analytic method to calculate the magnetic field generated by permanent magnet, we compiled a numerical tool for performing an intricate study of the mutual effect among the superconducting constituents in a superconducting levitation system with translational symmetry. Taking a superconducting unit with three constituents inside as a practice, we simulated the electromagnetic responses of this unit while moving in the nonuniform magnetic field generated by permanent magnet guideway and, identified the influences of the mutual effect on the levitation force as well as on the distributions of the magnetic flux density, the supercurrent density, and the levitation force density by comparing to an envisaged reference, one constituent was simulated with all the rest absent to remove the mutual effect. The insights attained by the present study, mostly being inaccessible from the experiments, are aimed to provide useful implications for the design of a superconducting levitation system for the transit and analogous purposes, which usually employ multiple superconductors to achieve the desired capability. [ABSTRACT FROM AUTHOR]

In the light of own measurements on a Faraday generator, the well-known theories concerning Unipolar Induction and the Faraday paradox seem to be problematic. On the other hand, all results obtained, and all other processes described as a paradox in connection with the Faraday generator can be explained without contradiction based on the theory of Wilhelm Weber. [ABSTRACT FROM AUTHOR]

Based on a publication of Assis, where the most straightforward and oldest motor is described, first constructed by Ampère, a simple experiment is added to demonstrate once again, why published explanations about its principle of operation and especial the kind how Newton's 3rd principle is used has to be rejected. Ampère's description of his motor and how it operates was explained in detail. [ABSTRACT FROM AUTHOR]

We review new electrodynamics models of interacting charged point particles and related fundamental physical aspects, motivated by the classical A.M. Ampère magnetic and H. Lorentz force laws electromagnetic field expressions. Based on the Feynman proper time paradigm and a recently devised vacuum field theory approach to the Lagrangian and Hamiltonian, the formulations of alternative classical electrodynamics models are analyzed in detail and their Dirac type quantization is suggested. Problems closely related to the radiation reaction force and electron mass inertia are analyzed. The validity of the Abraham-Lorentz electromagnetic electron mass origin hypothesis is argued. The related electromagnetic Dirac–Fock–Podolsky problem and symplectic properties of the Maxwell and Yang–Mills type dynamical systems are analyzed. The crucial importance of the remaining reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized.

Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E-fields and B-fields and that Faraday's Law can be derived without any relativistic assumptions about Lorentz invariance. It also widens the choice of axioms, or starting points, for understanding electromagnetism. This article is part of the theme issue 'Celebrating 125 years of Oliver Heaviside's 'Electromagnetic Theory''. [ABSTRACT FROM AUTHOR]

A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday’s and Ampere’s laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier–Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed. [ABSTRACT FROM AUTHOR]

This is a short article which utilizes the equations of Faraday’s law, Ampere’s law, and Ohm’s law. We manipulate the formulas to solve a practical application in which the electromotive force must be calculated. With the successful calculation of the electromotive force, we can use this technique in larger applications.

This paper deals with the numerical modeling of magnetohydrodynamics (MHD) phenomenon inside a nozzle arc. Previous work for MHD simulation shows that current density is computed from current continuity equation and thereafter the magnetic field is computed by either of the three approaches: A1-Biot-Savart Law; A2-magnetic vector potential equation; and A3-Ampere's Law. An alternative approach-called here as A4-is proposed here for nozzle arc application. This approach starts with computation of magnetic field from magnetic induction equation, and then current density is computed from Ampere's Law. The proposed approach is shown to give good agreement with other approaches (reported in the published literature) for low- as well as high-current applications. It is demonstrated that the A4 approach offers two advantages over the most commonly used A2 approach: 1) A4 approach achieves almost same computational accuracy with much less computation time and is thus numerically more efficient and 2) A4 approach is mathematically more efficient as it can be nondimensionalized and used for parametric investigation. A hybrid model is also proposed to demonstrate that the A4 model predicts arc characteristics accurately with little effect of singularity issue. [ABSTRACT FROM PUBLISHER]

In this work, an ultra low power all-MOSFET based current reference circuit, developed in 0.18 µm CMOS technology, is presented. The proposed circuit is based on the classical resistor-less beta multiplier circuit with an additional temperature compensation feature. The circuit is capable of providing the reference current in a nanoampere range for the supply voltage ranging from 1 V to 2 V in the industrial temperature range of −40 °C to 85 °C. The measurements were performed on 10 prototypes. The measured mean value of the reference current is 58.7 nA with a mean temperature coefficient value of 30 ppm/°C. In addition, the measured mean line regulation is 3.4%/V in the given supply voltage range. The total current consumption of the circuit is 352 nA and the chip area is 0.036 mm 2 . [ABSTRACT FROM AUTHOR]

We show here a “weak” Hölder regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge–Ampère equation with data in the L p space and Ω satisfying an f -property. The f -property is a potential-theoretical condition that holds for all pseudoconvex domains of finite type and many examples of infinite-type ones. [ABSTRACT FROM AUTHOR]

The existing literature about displacement current, although it is clearly defined, there are not enough publications clarifying its nature. Usually it is assumed that the electrical current is three types: conduction current, convection current and displacement current. In the first two cases we have directed movement of electrical charges, while in the third case we have time varying electric field. Most often for the displacement current is talking in capacitors. Taking account that charge carriers (electrons and charged particles occupy the negligible space in the surrounding them space, they can be regarded only as exciters of the displacement current that current fills all space and is superposition of the currents of the individual moving charges. For this purpose in the article analyzes the current configuration of lines in space around a moving charge. An analysis of the relationship between the excited magnetic field around the charge and the displacement current is made. It is shown excited magnetic flux density and excited the displacement current are linked by Ampere’s circuital law. [ABSTRACT FROM AUTHOR]

Our understanding of the universe at large and small scales relies largely on electromagnetic observations. As photons are the messengers, fundamental physics has a concern in testing their properties, including the absence of mass. We use Cluster four spacecraft data in the solar wind at 1 AU to estimate the mass upper limit for the photon. We look for deviations from Ampère’s law, through the curlometer technique for the computation of the magnetic field, and through the measurements of ion and electron velocities for the computation of the current. We show that the upper bound for m γ lies between 1.4 × 10 − 49 and 3.4 × 10 − 51 kg, and thereby discuss the currently accepted lower limits in the solar wind. [ABSTRACT FROM AUTHOR]

Internal microstructure evolution during alumina microwave sintering was in situ investigated with synchrotron radiation computed tomography (SR-CT). Two special microstructure evolution phenomena were continuously observed from the experimental images of the sample at different sintering times throughout the entire process of the sintering, which we called “suppressed particle growth” and “particle homogenization”. These two special phenomena were further confirmed by the two curves of “average particle radius” and “particle radius standard deviation” versus sintering time which were directly extracted from the full-field SR-CT results. A polarization Ampere’s force model was proposed to provide a possible explanation for these special phenomena, which introduced the effect of magnetic field on insulating ceramic materials, a topic rarely discussed in previous studies. The polarization Ampere’s force model may explain these two special sintering phenomena observed in the in situ experiment. On one hand, ceramic particles may sustain “Ampere’s force” that pointed toward the particle center according to this model, thereby possibly leading to the special suppressed-particle-growth phenomenon; on the other hand, large particles may sustain a strong force in our model, which may explain the other special phenomenon of particle homogenization. In return, these two special phenomena can also serve as probable experimental evidence of our polarization Ampere’s force model. This study may offer some help for revealing the complex mechanisms during microwave sintering and for preparing materials with expected microstructure and excellent properties. [ABSTRACT FROM AUTHOR]

Our raw intuition tells us that the topology of the universe shouldn't affect the behavior of a current-carrying wire, but when the wire wraps all the way around a multiconnected space, our intuition is wrong. While an infinitely long perfectly conducting wire in Euclidean space may carry a constant current, a simple application of the Ampére-Maxwell circuital law shows that the analogous wire in a 3-torus may not. Instead, we find that the current spontaneously oscillates, and the wire acts like an antenna, gradually radiating away its energy. [ABSTRACT FROM AUTHOR]

We develop a new time-domain method that is naturally matrix free, i.e., requiring no matrix solution, regardless of whether the discretization is a structured grid or an unstructured mesh. Its matrix-free property, manifested by a naturally diagonal mass matrix, is independent of the element shape used for discretization and its implementation is straightforward. No dual mesh, interpolation, projection, and mass lumping are required. Furthermore, we show that such a capability can be achieved with conventional vector basis functions without any need for modifying them. Moreover, a time-marching scheme is developed to ensure the stability for simulating an unsymmetrical numerical system whose eigenvalues can be complex-valued and even negative, while preserving the matrix-free merit of the proposed method. Extensive numerical experiments have been carried out on a variety of unstructured triangular, tetrahedral, triangular prism element, and mixed-element meshes. Correlations with analytical solutions and the results obtained from the time-domain finite-element method, at all points in the computational domain and across all time instants, have validated the accuracy, matrix-free property, stability, and generality of the proposed method. [ABSTRACT FROM AUTHOR]

This paper reviews the deduction of Ampère's law as made by Ampère himself, and following the same sequence of steps. We indicate the principles on which the law is founded. The expression of the law is the result of an interaction between experiment, and Ampère's skills to account for facts in the language of mathematics. [ABSTRACT FROM AUTHOR]

We provide a rejoinder to a review (Rosen, 2015) of our original article “Making or breaking climate targets — the AMPERE study on staged accession scenarios for climate policy” (Kriegler et al., 2015a). We have a substantial disagreement with the content of the review, and feel that it is plagued by a number of misconceptions about the nature of the AMPERE study and the integrated assessment modeling approach employed by it. We therefore see this rejoinder as an opportunity to clarify these misconceptions and advance the debate by providing a clearer understanding of the strengths, weaknesses, and ultimately the value of integrated assessment. [ABSTRACT FROM AUTHOR]

In this paper, a 220-V resistive superconducting fault current limiter (SFCL) prototype is built and tested under different prospective fault currents, which vary from 0.8 to 7.4 kA. A 2D superconductor model is integrated into an experimental circuit model in COMSOL to simulate the performance of the SFCL prototype in the experimental system in fault tests. In the simulation, a new E- J relationship is proposed to enhance the convergence of calculation. Comparison between simulation results and experimental results shows that the proposed model performs well in simulating current limiting performance of SFCL in experimental system in case of fault. [ABSTRACT FROM AUTHOR]

A novel magnetic field sensor using distributed Bragg reflector (DBR) fiber laser by Ampere's force effect is proposed and experimentally demonstrated. The key sensing element, that is the dual-polarization DBR fiber laser, is fixed on the middle part of two copper plates which carry the current. Ampere's force is applied onto the coppers due to an external magnetic field generated by a DC solenoid. Thus, the lateral force from the coppers is converted to a corresponding beat frequency signal shift produced by the DBR laser. The electric current sensing is also realized by the same configuration and same principle simultaneously in an intuitive manner. Good agreement between the theory calculation and the experimental results is obtained, which shows a good linearity. This sensor's sensitivity to the magnetic field and to the electric current finally reaches ~258.92 kHz/mT and ~1.08727 MHz/A, respectively. [ABSTRACT FROM AUTHOR]

In this paper, it presented a device intended to reproduce magnetic fields of differents shapes to help the test or calibration of current measuring instruments based on Ampere's Law (current transformers, current clamps, and Rogowsky probes). In particular, this device can reproduce the effect of uncentered currents without requiring any mechanical displacement of the conductor or the device under test during its operation. Any uncentered or distributed current is approximated by a linear combination of currents flowing along a specific set of conductors. First, the theoretical vectorial analysis is presented, and second, a specific arrangement of conductors is used to illustrate the method. A number of measurements have been taken to check the results. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new kind of calibration method for current measuring instruments based on Ampere’s law (current transformers, current clamps, Rogowsky probes, and so on) is proposed. The method focuses in the uncertainty associated to the geometric variability of the circuits where the current is to be measured and it does not require to perform any mechanical displacements of the instrument. It is based on the fact that the relevant magnetic effect of a circuit over a measuring instrument is the tangential component of the magnetic strength along the Ampere’s law integration path. This effect can be recreated by the sum of the magnetic effects of a set of predefined circuits, each one excited by a specific current (and different for each circuit to recreate). The method also offers a graphical representation of the instrument response variability when off center indefinite straight wires are applied. An experimental setup and finite-element method simulations have been used to check the results. [ABSTRACT FROM PUBLISHER]

Nanospintronic and related research often requires the application of quickly rising magnetic field pulses in the plane of the studied planar structure. We have designed and fabricated sub-millimetersized coils capable of delivering pulses of the magnetic field up to ~500 Oe in the plane of the sample with the rise time of the order of 10 ns. The placement of the sample above the coil allows for easy access to its surface with manipulators or light beams for, e.g., Kerr microscopy. We use the fabricated coil to drive magnetic domain walls in 1 μm wide permalloy wires and measure magnetic domain wall velocity as a function of the applied magnetic field. [ABSTRACT FROM AUTHOR]

This paper provides an overview of the AMPERE modeling comparison project with focus on the implications of near-term policies for the costs and attainability of long-term climate objectives. Nine modeling teams participated in the project to explore the consequences of global emissions following the proposed policy stringency of the national pledges from the Copenhagen Accord and Cancún Agreements to 2030. Specific features compared to earlier assessments are the explicit consideration of near-term 2030 emission targets as well as the systematic sensitivity analysis for the availability and potential of mitigation technologies. Our estimates show that a 2030 mitigation effort comparable to the pledges would result in a further “lock-in” of the energy system into fossil fuels and thus impede the required energy transformation to reach low greenhouse-gas stabilization levels (450 ppm CO 2 e). Major implications include significant increases in mitigation costs, increased risk that low stabilization targets become unattainable, and reduced chances of staying below the proposed temperature change target of 2 °C in case of overshoot. With respect to technologies, we find that following the pledge pathways to 2030 would narrow policy choices, and increases the risks that some currently optional technologies, such as carbon capture and storage (CCS) or the large-scale deployment of bioenergy, will become “a must” by 2030. [ABSTRACT FROM AUTHOR]

It is shown that the application of hydrodynamic equations allows to obtain analogous to electrodynamics results for the Ampere forces. They are connected with the Joukowski force. Equations for analogs to electromagnetic waves follow from consideration of acoustic waves propagation in the physical vacuum. Problems connected with electromagnetic energy are considered. [ABSTRACT FROM PUBLISHER]

In this paper, induction is studied only with the appropriate forces on each standing/ moving charge by all other standing/moving charges and not by any magnetic field or mysterious flux. These appropriate forces should be called with the older term "Electro-Motive Forces" (EMF). Maxwell, the Father of Modern Electromagnetism, who principally only had experience with DC currents in batteries, claimed three inaccurate theses: (1) Every current belongs to a closed circuit, (2) every current is the same all along a circuit, and (3) the Ampère force law is equivalent to the Lorentz force law, and therefore, the Ampère law should be considered redundant, all of which are propagated today. Realizing the actual inaccuracy of those three cases and taking into account the Ampère Cardinal Force Law, superior electrodynamics arises. In particular, consider the following: (a) A static conductor with AC, with current that is not DC battery current, or (b) a DC conductor moving perpendicularly, which produces a nonclosed secondary current perpendicular to the conductor. Taking into account Ampère's absolute, Non-Relativistic, Electrodynamic Cardinal Law [J. M. Ampère, French Academy of Science, 1821-1826; R. A. R. Tricker, Early Electrodynamics (Pergamon Press, New York, 1965), p. 49,55] on other closed or open circuits, proof and prediction of all details of Faraday's empirical induction law, the Lentz empirical rule is produced for the first time. These laws gave the wrong impression to Einstein ([Ann. Phys. 18,639,1905], electrodynamics for the moving bodies, with similar title and exact subject as Lorentz's [H. A. Lorentz, in Proceedings of the Royal Netherlands Academy of Arts and Sciences, Vol. 6, pp. 809-831 (KNAW, Amsterdam, Netherlands, 1904), http://en.wikipedia.org/wiki/Lorentz_ether_theory], electromagnetic phenomena in a system moving with any velocity smaller than that of light) since as early 1892 and 1895 and finally 1904, prior to Einstein's paper in 1905 [A. Einstein, Ann. Phys. 18,639 (1905)], for the foundations of Special Relativity. In addition, Ampère's absolute-nonrelativistic, Electromotive Force Law exclusively provides the real analytical distribution [F. J. Müller, Galilean Electrodyn. 1, 27 (1990); W. Panofsky and M. Phillips, Classical Electricity And Magnetism (Addison- Wesley, Reading, MA, 1962), Sec. 18-6; F. J. Müller, see http://www.worldnpa.org/pdf/abstracts/ abstracts_113.pdf for an experimental disproof of special relativity theory (unipolar induction), 2013; F. J. Moller, Galilean Electrodynamics, http://home.comcast.net/~adring/muller.htm, 2013] of induction potential, which, for the very first time, is determined. The wrongly assumed equivalent. Lorentz Law cannot determine this fact! Ampère's Law and its modifications by the present authors always retain the principle of action-reaction and momentum; in contrast to the Law of Lorentz which is violating the conservation of momentum and angular momentum. Thus, the Law of Lorentz cannot replace Ampère's Law. Ampère's law may predict the propagation of electromagnetic near field waves (see, Electrodynamic ± Force Near Field Waves section), or better ± electrodynamic force near field waves, without Maxwell's equations. We use the term "electrodynamic" for the magnetic field of a changing current that is not what we suppose it to be for nonclosed currents with quickly changing currents. For such currents, a current change cannot instantaneously occur at every point of a circuit, as it takes time to propagate, despite Maxwell's considerations. Maxwell did not know of Tesla's alternating currents during his time; rather, he knew only of batteries with DC constant currents. A changing AC current along a circuit cannot have the same value everywhere because of the finite propagation of the current (see also the experiments and measurements of Pappas [P. T. Pappas and T. Vaughan, Phys. Essays 3, 211, 1990, P. T. Pappas, see www.panospappas.gr for schematics 4A, 4B, 2014]. Therefore, current changes cannot have instantaneous propagation, making the current vary throughout its circuit. Therefore, a ± electrodynamic near field force interaction wave may naturally be expected for such AC currents but not for DC currents according to the absolute-nonrelativistic law of Ampère. In both AC producing electromagnetic near field wave currents and DC nonproducing electromaga netic near field currents, DC and AC are different types of currents with different results; nevertheless, these differences do not affect the relativistic Lorentz Law. The theory of relativity is irrelevant to this thesis, and relativity's founding considerations are proven incorrect [F. J. Müller, Galilean Electrodyn. 1, 27 (1990); F. J. Müller, See http://www.worldnpa.org/pdf/abstracts/ abstracts_113.pdf for an experimental disproof of special relativity theory (unipolar induction), 2013]. Ampère electrodynamics is meant to replace Maxwell's electromagnetism, with its illconceived theory of magnetic fields for individual moving charges, elementary particles and changing currents. [ABSTRACT FROM AUTHOR]

Knowledge is not simply a collection of facts, principles, and formulas; instead, meaningful knowledge is organized around core concepts that guide peoples' thinking about a subject. Therefore, knowledge organization is recognized as an important component of understanding learning and teaching. In this research, knowledge organization of two physics university textbooks was compared with that of four physics university teachers. The topic studied was magnetostatics with an emphasis on two topics of Biot-Savart law and Ampère's law. The aim of study was to examine the structural features of the subject matter knowledge of teachers and textbooks. For this reason, concept maps were utilized to picture clearly their knowledge organizations. Concept maps were evaluated by means of a focus on their structural characteristics including hierarchy and clustering. Results indicate that the hierarchical organizations between knowledge of teachers and textbooks vary from one topic to another. The hierarchical organizations of teachers are more comparable to textbooks for the topic of Biot-Savart law. The clustering behaves in a very similar way in the case of patterns between textbooks and teachers for both topics. It was observed that the knowledge arrangements of Ampère's law were more hierarchical, while the knowledge organizations of Biot-Savart were more clustered. Moreover, structural properties varied from one topic to another, even though topics belong to the same context. The possibility of recognizing such difference in knowledge organization is a first step towards developing more effective teaching and learning solutions. [ABSTRACT FROM AUTHOR]

We performed a new coupled circuit numerical simulation of eddy currents in an open compact magnetic resonance imaging (MRI) system. Following the coupled circuit approach, the conducting structures were divided into subdomains along the length (or width) and the thickness, and by implementing coupled circuit concepts we have simulated transient responses of eddy currents for subdomains in different locations. We implemented the Eigen matrix technique to solve the network of coupled differential equations to speed up our simulation program. On the other hand, to compute the coupling relations between the biplanar gradient coil and any other conducting structure, we implemented the solid angle form of Ampere's law. We have also calculated the solid angle for three dimensions to compute inductive couplings in any subdomain of the conducting structures. Details of the temporal and spatial distribution of the eddy currents were then implemented in the secondary magnetic field calculation by the Biot--Savart law. In a desktop computer (Programming platform: Wolfram Mathematica 8.0®, Processor: Intel(R) Core(TM)2 Duo E7500 @ 2.93 GHz; OS: Windows 7 Professional; Memory (RAM): 4.00 GB), it took less than 3 min to simulate the entire calculation of eddy currents and fields, and approximately 6 min for X-gradient coil. The results are given in the time--space domain for both the direct and the cross-terms of the eddy current magnetic fields generated by the Z-gradient coil. We have also conducted free induction decay (FID) experiments of eddy fields using a nuclear magnetic resonance (NMR) probe to verify our simulation results. The simulation results were found to be in good agreement with the experimental results. In this study we have also conducted simulations for transient and spatial responses of secondary magnetic field induced by X-gradient coil. Our approach is fast and has much less computational complexity than the conventional electromagnetic numerical simulation methods. [ABSTRACT FROM AUTHOR]