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В статье выполнен критический анализ современного подхода и предложен более простой и физически содержательный метод доказательства теоремы Ампера (закона полного тока). On the buse of modern approach critical analysis the article demonstrate new, more simple and physically consistent method of Ampere’s theorem (Full Current Law) verification proof.

В статье выполнен критический анализ современного похода и предложен более простой и физически содержательный метод доказательства теоремы Ампера (закона полного тока)., On the buse of modern approach critical analysis the article demonstrate new, more simple and physically consistent method of Ampere’s theorem (Full Current Law) verification proof.

The right steps to follow for a Finite Element Analysis (F.E.A) applied to a linear actuator used for biomedical application are represented in this paper. The Ampere's theorem is detailed in order to prove the essential role of the air gap. The position reached by the actuator using an analog sensor is compared to the ones with Matlab and the finite element software from INFOLYTICA. The alloys from AK Steel company were introduced to choose the high permeability material for a best magnetic performance. The desired position of 100 mils which is equal to 2.54 mm is reached by three different methods starting by Matlab simulation and was confirmed by both of the Finite Element Methods and an experimental test using an analog position sensor. In this paper, a complete research of the linear actuator is proposed which encompasses all the subjects and considered as a sample to follow.

The Matrix Pencil method is used for extracting maximum information from the Electro-Magnetic disturbances emitted by power converters; these disturbances are manifested by an induced current in electric systems located in the power converter environs. The modeling of the power converter in time domain is realized by solving Maxwell’s equations which allow determining the radiated electromagnetic field, Ampere’s theorem is then used for computing the induced current in passive loops representing the victim system. In our work we also analyze the effect of the geometric configuration for both the passive loops and the power converter by extracting the poles and residues using Matrix Pencil method.

PurposeTo model magneto‐harmonic devices including solid conductors with holes when the skin depth is very small.Design/methodology/approachThe 3D finite element magnetic scalar potential formulation combined with the surface impedance condition approximation is used. It allows the modelling of thin skin depth effect at low cost.FindingsThe paper shows how to use surface impedance condition for solid conductors with holes, when using the magnetic scalar potential. Specific equations must be added to respect Ampere's theorem. The paper establishes these equations and the coupling with the finite element formulation. The final system of equations is symmetric.Research limitations/implicationsThe formulation allows to treat linear material in the magneto‐harmonic assumption.Originality/valueThe use of surface impedance condition with the 3D finite element magnetic scalar potential formulation is well known. The originality is to take into account holes (multiply connected conductors).

International audience; This paper presents an electromagnetic analytical model for a Permanent Magnet Assisted Synchronous Reluctance Motor (PMA-SRM). The proposed model is based on the Maxwell equations: Ampere's theorem and the flux conservation law. The stator and rotor magnetic saturation are considered, as well as the effect of the magnetic bridges of the flux barriers. The goal is to compute the motor performances (average torque, voltage and power factor) for several current values and current angles. The analytical model results are compared to those from a Finite Element Model (FEM) and are subsequently validated by an experimental prototype.

The current and field profiles of a uniform resistively shunted Josephson-junction array (JJA) are calculated from the AC and DC Josephson equations, Ampere's theorem, and gauge-invariant phase difference. After a sudden rise of the applied field, AC Josephson currents shield the interior of the JJA, which is followed by two distinct processes, ending with either an oscillatory DC current profile when the critical current I 0 of each junction is small or a critical-state type of current shielding when I 0 is large. The latter can be the basis for understanding the intergranular critical state in high- T c superconductors.

Fibre optical current sensor (FOCS) is a promising alternative to inductive sensors for the measurement of the plasma current in future thermonuclear fusion reactors. Standard FOCS relies on the measurement of the state of polarisation (SOP) of light at the output of an optical bre surrounding a current. Because of the Faraday eect, magnetic eld induced by electrical current rotates the SOP of light travelling into the bre. According to the Ampere's theorem this rotation is proportional to the surrounded current. In future tokamaks like ITER and DEMO, the plasma current will be suciently high to generate a rotation of the SOP higher than 2 radians. These conditions may lead to uncertainties on the determination of the plasma current if no post processing is performed. In this paper we propose a solution with a Polarisation Optical Time Domain Re ectometer (POTDR) setup allowing both unambiguous plasma current measurement and also local magnetic eld measurements. This measurement is based on the assessment of the SOP rotation of the Rayleigh backscattered POTDR signal. Thanks to the presence of an input polarizer, SOP variations are converted into power uctuations that contain information about the distribution of the magnetic eld and therefore about the plasma current. Using the Jones formalism we have developed a model accounting for the modication of the SOP of light travelling into the optical bre and the evolution of the POTDR signal. In parallel experimental PODTR measurements have been performed on the Tore Supra tokamak situated at CEA Cadarache in France. A comparison between the models and the experimental results conrms the capability of the system to measure the plasma current and the local magnetic eld even if further data post processing are still required.

В статье выполнен критический анализ современного похода и предложен более простой и физически содержательный метод доказательства теоремы Ампера (закона полного тока). В статті виконано критичний аналіз сучасного підходу, а також запропоновано більш просту та фізично змістовну методу доказу теореми Ампера (закону повного струму). On the buse of modern approach critical analysis the article demonstrate new, more simple and physically consistent method of Ampere’s theorem (Full Current Law) verification proof.

We consider the magnetostatic response to an external magnetic field of a crystal containing off-center ions, such as Li^+ in KCl and KBr or the apical oxygens O(A) in the LaSCO family of layered perovskites. Magnetic dipoles are deduced from the matrix elements of the energy operator of a spinning particle in a magnetic field which particle also satisfies the nonlinear Mathieu equation. The magnetic moments are found to increase in magnitude as the system goes from the lowest energy ground state to the higher lying excited states. Our conclusions are in concert with earlier studies of magnetic dipoles from circular currents based on Ampere's theorem., Comment: 9 pages of wording including 1 appendix, and 7 figures, all pdf format

Publisher Summary This chapter describes eddy-current scattering. The analysis so far has shown that both finite element methods and integral methods make it possible to model eddy currents in a damaged structure with a fair accuracy and to appraise the physical phenomenon behind the often elaborated functional theory. The formulations are naturally amenable to discrete approximations, which boil down to replacing the infinite-dimensional function space in which they are developed with a finite-dimensional subspace onto which they are projected. Variational formulations of three-dimensional eddy current problems can be classified into two dual families. One family works with the variables of the system of Ampere's theorem, the other works with the variables of the system of Faraday's law. In these formulations, different choices of unknown variables in conducting regions are possible. They can be in terms of field or potential variables.

A direct application of Ampere's theorem enables us to calculate the total amount of electric current passing through the plane enclosed by the MAGSAT orbit, through the line-integration of the observed magnetic field component tangential to the MAGSAT orbit. After eliminating the spurious effect arising from the earth's rotation under the MAGSAT orbit, it is concluded that the space current of a few million A flows anti-sunward below the MAGSAT level during magnetic storms in good correlation with the AE-index, whereas such a space current is almost absent under quiet conditions. The existence of an anti-sunward space current on disturbed days gives a strong support to the development of a partial ring current in the magnetosphere during magnetic storms.

SUMMARY. — The author has aimed at showing that the theorem which is known as Ampere's Theorem, an admirable expression of his deepest thought, cannot have been stated by Ampère himself. As can be established by an unpublished document in the archives of the Académie des Sciences, it is Ampere's physical theory of magnetism itself which blocked his researches, and not difficulties of a mathematical nature. This article contains a comparison between Ampere's procedure in the unpublished document in the archives and Maxwell's in his Treatise on Electricity and Magnetism, concerning the problem of the action of an indefinite vertical current on a magnet pole., RÉSUMÉ. — L'auteur a voulu montrer que le théorème connu sous le nom de théorème ďAmpère, qui exprime admirablement le fond de sa pensée, ne pouvait pas être énoncé par Ampère lui-même. Comme permet de l'établir un inédit des Archives de l'Académie des Sciences, c'est la théorie physique même du magnétisme d'Ampère qui a bloqué ses recherches, et non des difficultés d'ordre mathématique. On trouvera, dans ce travail, une comparaison entre la démarche d'Ampère dans l'inédit des Archives et celle de Maxwell dans son Traité ďélectricité et de magnétisme, relative au problème de l'action d'un courant vertical indéfini sur un pôle d'aimant., Hamamdjian Pierre Gerard. Contribution d'Ampère au « théorème d'Ampère ».. In: Revue d'histoire des sciences, tome 31, n°3, 1978. pp. 249-268.

International audience; This paper presents a non-linear analytical model of a multi-V-shape Interior Permanent Magnet (IPM) motor with non-overlapping concentrated winding. The model relies on Ampere's theorem and the flux conservation law in order to compute the flux density in the different parts of the motor. This article proposes a saturated analytical model of the stator and the rotor. The analytical model is used to calculate the average torque, the power factor and the voltage of the motor. It is 5 times faster than the 2D Finite Element Analysis (FEA). The results are compared to 2D FEA simulations and experimentally validated using a prototype motor.

It is possible to calculate, with the Magsat data, the total amount of electric current passing through the plane enclosed by the Magsat orbit, from the line integration of the observed magnetic field component tangential to the Magsat orbit, i.e., a direct application of Ampere's theorem. After eliminating the spurious effect arising from the earth's rotation under the Magsat orbit, it is concluded that the space current of a few million amp. flows antisunward below the Magsat level during magnetic storms, whereas such a space current is almost absent on quiet condition. The depression in the horizontal intensity of geomagnetic field in low latitudes is noticeably greater on the duskside than on the dawnside, especially at the developing stages of magnetic storms. Combining these two observations, we may conclude that 10--20% of the westward ring (or shell) current in the dusk magnetosphere will close its current circuit with antisunward field-aligned current in the magnetosphere connected with a net horizontal current flowing in the ionosphere.

ACCORDING to Ampere's theorem, the magnetic field due to an electric current flowing in any circuit is equivalent at external points to that due to a simple magnetic shell the bounding edge of which coincides with the conductor, and the strength of which is equal to the strength of the current.