


Politecnico di Torino  
Academic Year 2009/10  
13AUQFD Fundamental of Electrotechnics II 

1st degree and Bachelorlevel of the Bologna process in Electrical Engineering  Torino 





Objectives of the course
The aim of the corse is the introduction to quasi stationary fields for the electrical engineering applications: electrostatic fields, static current fields, magneto static fields, quasi stationary electromagnetic fields.

Expected skills
The course will introduce to static and quasi static field problems. Analysis of simple geometric situations and evaluation of integral parameters like capacitance, conductance, ground resistances. Introduction to magnetic circuits. Magnetic fields in air and inductive models of electric lines. Introduction to electromechanics.

Prerequisites
Eletcrotechnics (circuit theory); Physics.

Syllabus
Introduction ro scalar and vectorial fields. First order differential operators: gradient, divergence, curl and main theorems involved. Second order differential operators: Laplace, Poisson problems. Use of potentials and Helmotz theorem.
Electrostatic field: equations properties of materials and continuity conditions between different material susceptibility. Case of a point charge source. Application of superposition principle. Electric dipole. Image principle applications: field between two spheric armatures and capacitance. Field generated by a segment uniform charge: potential evaluation and capacitance prediction. Line uniform charge distribution and electric field: field and capacitance evaluation in the case of cylindrical armatures disposed according parallel axes. Plane ground effects. Simplified case of cylindrical conductors and capacitance coefficients evaluation. Multiconductor representation by means of a capacitance matrix. Static current field: equations and continuity conditions. The case of current flux tubes conductance evaluation. The case of metallic conductors embedded in the ground: image principles. Elementary geometries: conductive sphere in an unlimited homogeneous ground, sphere buried into the ground at a stated distance, ground rod, horizontal wire, more electrodes connected in parallel a simplified approach to electrodes interaction. Touch and step voltages prediction. Measure of a ground resistance. Introduction to static magnetic fields: equations and continuity conditions between different media. Magnetic fields into flux paths: magnetic circuit approach, equations, reluctance model, Hopkinson method. Use of hard magnetic materials in a magnetic circuit. Magnetic fields in homogeneous media: Biot and Savart formula: example of a circular wire. Quasi static electromagnetic field, scalr and vector potentials: Faraday law and introduction of self and mutual inductances. Magnetic circuits cases and the interaction among electric and magnetic circuits. The case of quasi stationary field in air and the model of multiconductor systems according to Neumann formula. Electric lines inductive model. Mechanical interaction between field and currents. Introduction to electromechanics. Skin effect in a unlimited conductor according a 1D magnetic and electric field distribution. Effects of variable magnetic fields in magnetic cores a simplified approach. 
Syllabus: more informations
The professor and his assistant will be available one hour before and after any lesson.
An appointment will be possible by means of email communications. 
Laboratories and/or exercises
Laplace and Poisson solution in a simple spherical coordinate system.
Image charges with respect to planes. Sphere gaps. Simple capacitances: plane armatures and cylindrical case. Electric field generated by a linear chrge distribution. Electric line field. Cylindrical armatures capacitances and fields. Current fields in the ground with simple grounding system geometries. Interaction among grounding systems: a simple approach. Magnetic circuit: equations with and without permanent magnetic materials. Faraday law: application to magnetic circuits: self and mutual inductance evaluation. Electric lines evaluation of magnetic fields and of self and mutual inductances. Electromechanics: forces on conductors and parts of magnetic circuits (electromagnets). 
Bibliography
L. Piglione, 'Elettrotecnica: FiltriLineeCampi', Levrotto & Bella, Torino (esaurito).
K. Kupfmüller, 'Fondamenti di Elettrotecnica', UTET, Torino, 1968. C.R. Paul, K. W. Whites, S.A. Nasar, 'Introduction to Electromagnetic Fields', Mc GrawHill, 2000. D. K. Cheng, ' Field and Waves Electromagnetics', AddisonWesley publishing Company, 1996. M. D'Amore, 'Elementi di Elettrotecnica: Campi e Circuiti', edizioni scientifiche SIDEREA, Roma, 1995. A. Canova, G. Gruosso, M. Tartaglia, 'Esercitazioni di Elettrotecnica: Linee e campi', Levrotto & Bella, Torino, 2003. 
Check availability at the library 
Revisions / Exam
Written and oral tests. The oral test is allowed if a minimum threshold will be overcome (>13/30).

