Abstract-The production of magnetic forces in a magnetic actuator is the focus of the present analysis. Magnetic circuit analysis is used to investigate the direction as well as the expected order of magnitude of the force that attracts the armature into the central portion of a stationary core. A sequence of finite-element based solutions is used to investigate magnetic saturation and to determine the forcedisplacement characteristic. The analytical approach is based on the principle of virtual work and Ampère's law. The force calculations based on numerical field solutions employ the methods of weighted Maxwell stress tensor and the classical virtual work. The more accurate field-derived solutions are used to explain the limitations of the analytical calculations. At the end, an alternative approach to compute the force numerically is proposed. This method is based on the principle of virtual work, but only one field solution is required.Index Terms-Energy storage, finite element methods, magnetic circuits, magnetic forces.

A nova geração de simuladores de campos eletromagnéticos pode ser usada no ensino de eletromagnetismo sem que o usuário conheça com profundidade a metodologia usada no desenvolvimento desses programas computacionais. A teoria da linha coaxial cilíndricaé usada para ilustrar a aplicação desses programas como ferramenta de ensino. A solução analítica do problemaé usada para avaliar a precisão numérica dos resultados obtidos utilizando diferentes subdivisões das malhas de elementos finitos. A relação entre minimalidade energética e distribuição de potenciais elétricosé usada para explicar como diferentes discretizações do modelo afetam o cálculo das grandezas eletromagnéticas. A definição de um problema exterior para modelar a estrutura coaxial permite a análise dos campos dispersos nas extremidades e aumenta a precisão do cálculo da capacitância. Palavras-chave: axissimetria, campos elétricos, método dos elementos finitos, método variacional.The new generation of electromagnetic field simulators can be used for teaching electromagnetism with no user's deep knowledge about the methodology used to develop these computer programs. The theory of the cylindrical coaxial line is used to illustrate the application of these programs as teaching tools. The analytical solution of the problem is used to assess the accuracy of the numerical results produced by different subdivisions of the finite element meshes. The relationship between energy minimality and distribution of electric potentials is used to explain how different discretizations of the model affect the computation of the electromagnetic variables. The definition of an exterior problem to model the coaxial structure allows the analysis of leakage fields at the end-zone and improves the accuracy of capacitance calculation.

The paper describes an approach to teaching mutually-coupled circuits CAD techniques to undergraduate students pursuing a degree course in electrical engineering or physics, and explains how a series of simulated experiments may be incorporated into the existing subjects. The simulated experiments make use of a two-dimensional open-access software based on the finite-element method. At the laboratory meetings, the students learn how to set up field problems for solution, and how to examine the results. Simulation tasks based on three axisymmetric open-boundary problems are used to introduce different numeric techniques to compute inductance and magnetic forces. The paper takes the reader to a step-by-step simulation journey, and provides all the basic elements required for further exploration of axially-symmetric systems.

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