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# Ampère's circuital law

About: Ampère's circuital law is a research topic. Over the lifetime, 103 publications have been published within this topic receiving 796 citations. The topic is also known as: '''Ampère's circuital law'''.

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TL;DR: In this paper, an analytical model for double-sided permanent-magnet radial-flux eddy-current couplers is presented that can easily handle complex geometries.

Abstract: Analytical models are widely utilised in the study and performance prediction of electric machines by providing fast, yet accurate solutions. By combining conventional magnetic equivalent circuit techniques with Faraday's and Ampere's laws, an analytical model for double-sided permanent-magnet radial-flux eddy-current couplers is presented that can easily handle complex geometries. The proposed approach is also capable of taking the three-dimensional (3D) impacts into account. The characteristics and design considerations are also studied for a surface-mounted permanent-magnet structure. Moreover, the 2D and 3D finite-element methods are employed to verify the results, as well as transient study of the device under two different scenarios. Finally, sensitivity analysis is carried out to investigate the influence of the design variables on the characteristics of the coupler, which provides valuable information in the current and future studies of such devices.

62 citations

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16 Nov 2009

TL;DR: In this paper, the authors propose a vector analysis of the Maxell s Equations for a system of charges and a solution of the Inhomogeneous Wave Equation with inhomogeneous Boundary Conditions.

Abstract: Acknowledgments. Introduction. 1 Foundations of Maxwell s Equations. 1.1 Historical Overview. 1.2 Role of Electromagnetic Field Theory. 1.3 Electromagnetic Field Quantities. 1.4 Units and Universal Constants. 1.5 Precision of Measured Quantities. 1.6 Introduction to Complex Variables. 1.7 Phasor Notation. 1.8 Quaternions. 1.9 Original Form of Maxell s Equations. 2 Vector Analysis. Introduction. 2.1 Addition and Subtraction. 2.2 Multiplication. 2.3 Triple Products. 2.4 Coordinate Systems. 2.5 Coordinate Transformations. 2.6 Vector Differentiation. 2.7 Divergence Theorem. 2.8 Stokes's Theorem. 2.9 Laplacian of a Vector Field. 3 Static Electric Fields. Introduction. 3.1 Properties of Electrostatic Fields. 3.2 Gauss s Law. 3.3 Conservation Law. 3.4 Electric Potential. 3.5 Electric Field for a System of Charges. 3.6 Electric Potential for a System of Charges. 3.7 Electric Field for a Continuous Distribution. 3.8 Conductor in a Static Electric Field. 3.9 Capacitance. 3.10 Dielectrics. 3.11 Electric Flux Density. 3.12 Dielectric Boundary Conditions. 3.13 Electrostatic Energy. 3.14 Electrostatic Field in a Dielectric. Endnotes. 4 Solution of Electrostatic Problems. Introduction. 4.1 Poisson s and Laplace s Equations. 4.2 Solutions to Poisson s and Laplace s Equations. 4.3 Green s Functions. 4.4 Uniqueness of the Electrostatic Solution. 4.5 Method of Images. 5 Steady Electric Currents. 5.1 Current Density and Ohm s Law. 5.2 Relation to Circuit Parameters. 5.3 Superconductivity. 5.4 Free Electron Gas Theory. 5.5 Band Theory. 5.6 Equation of Continuity. 5.7 Microscopic View of Ohm s Law. 5.8 Power Dissipation and Joule s Law. 5.9 Boundary Condition for Current Density. 5.10 Resistance/Capacitance Calculations. Endnotes. 6 Static Magnetic Fields. Introduction. 6.1 Magnetic Force. 6.2 Magnetostatics in Free Space. 6.3 Magnetic Vector Potential. 6.4 The Biot-Savart Law. 6.5 Historical Conclusions. 6.6 Atomic Magnetism. 6.7 Magnetization. 6.8 Equivalent Surface Current Density. 6.9 Equivalent Magnetic Monopole Charge Density. 6.10 Magnetic Field Intensity and Permeability. 6.11 Ferromagnetism. 6.12 Boundary Conditions for Magnetic Fields. 6.13 Inductance and Inductors. 6.14 Torque and Energy. Endnotes. 7 Time-Varrying Fields. 7.1 Faraday s Law of Induction. 7.2 E&M Equations before Maxwell. 7.3 Maxwell s Displacement Current. 7.4 Integral Form of Maxwell s Equations. 7.5 Magnetic Vector Potential. 7.6 Solution of the Time-Dependent Inhomogeneous Potential Wave Equations. 7.7 Electric and Magnetic Field Equations for Source-Free Problems. 7.8 Solutions for the Homogeneous Wave Equation. 7.9 Particular Solution for the Inhomogeneous Wave Equation. 7.10 Time Harmonic Fields. 7.11 Electromagnetic Spectrum. 7.12 Electromagnetic Boundary Conditions. 7.13 Particular Solution for the Wave Equation with Inhomogeneous Boundary Conditions. 7.14 Memristors. 7.15 Electric Vector Potential. APPENDIX A: MEASUREMENT ERRORS. APPENDIX B: GRAPHICS AND CONFORMAL MAPPING. APPENDIX C: VECTORS, MATRICEES, ORTHOGONAL FUNCTIONS. BIBLIOGRAPHY. Index.

56 citations

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TL;DR: In this article, a closed form solution for the magnetic field intensity and current density in an electromagnetic railgun was presented for a simple geometrical design, where a constant velocity for the armature and constant material properties for the rail and armature have been assumed in all calculations.

Abstract: A closed form solution for the magnetic field intensity and current density in an electromagnetic railgun is presented for a simple geometrical design. A constant velocity for the armature and constant material properties for the rail and armature have been assumed in all calculations. Plots of the magnetic field, current densities, and current streamline are presented for a sample velocity and conductive material.

39 citations

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TL;DR: In this paper, the electric and magnetic fields of a point charge moving with constant velocity are derived from retarded integrals representing solutions of Maxwell's equations for electric and magnetic fields of arbitrary time-dependent charge and current distributions.

Abstract: Equations for the electric and magnetic fields of a point charge moving with constant velocity are derived from retarded integrals representing solutions of Maxwell’s equations for electric and magnetic fields of arbitrary time‐dependent charge and current distributions. In contrast to conventional derivations, the derivations presented here are based exclusively on general electromagnetic field equations and do not make use of retarded potentials or relativistic equations. The derivations lead to some notable conclusions concerning the electric and magnetic fields of an arbitrary charge distribution moving with constant velocity.

31 citations

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Nippon Steel

^{1}TL;DR: In this article, the fundamental equation for the A-phi method is formulated using Maxwell's equations and the continuity equation for electric charge, and the validity of the proposed formulation is verified by experiment.

Abstract: The fundamental equation for the A- phi method is formulated using Maxwell's equations and the continuity equation for electric charge. Maxwell's equations necessarily involve the continuity equation under the assumption that the displacement current can be ignored. However, in the finite element method, an acceptable solution cannot be obtained if the continuity equation is not treated as an independent equation. The situation is clarified theoretically, and the physical significance is discussed. A model of a conducting liquid in a moving magnetic field is analyzed, and the validity of the proposed formulation is verified by experiment. >

30 citations