FIELS ANALYSIS AND MODELLING FAM

1. FIELS ANALYSIS AND MODELLINGFAM Marilena STĂNCULESCU Electrical Engieering Faculty, Electrical Engineering Department, Office EB234 marilena.stanculescu@upb.ro

2. BIBLIOGRAPHY On-line resources: course T.R. Kuphaldt, Lessons in Electric Circuits A free series of textbooks on the subjects of electricity and electronics, Volume I – DC, Volume II – AC On-line resources: applications J.A. Svoboda, Electric Circuit Study Applets J.A. Svoboda, Interactive Examples & Exercises M.D. Filipovic, Understanding Electronics Components Amanogawa & Semchip, Circuit Applets (Power components for sinusoidal signal. Parallel and series resonant circuits) The Nuffield Foundation, Electric Circuits & Fields On-line resources: terminology, units CEI, The International System of Units and the IEC (USA) National Institute of Standards and Technology – NIST, Constants, Units & Uncertainty – CUU Text books, set of problems L. Ochiana, G. Ochiana, M. Stănculescu, Electromagnetic Field Theory, Ed. Pritech, Bucharest, 2012. M. Vasiliu, I.F. Hănţilă, Electromagnetics, Editura Electra, Bucureşti, 2006 E. Cazacu, I. Nemoianu, M. Maricaru, F. Enache, M. Stănculescu, A. Stănciulescu, A. Anghel, Chestiuni speciale de teoria circuitelor electrice – elemente de teorie şi aplicaţii, Editura Matrix-ROM, Bucureşti, 2005 E. Cazacu, Marilena Stănculescu, Bazele electrotehnicii – seminar, Editura Matrix Rom, Bucureşti, 2004.

3. ELECTROMAGNETIC FIELD THEORY – the basis of FAM Introduction Objective: an applicative approach of the electromagnetic field theory as a fundamental part of the vast domain of electrical engineering. • the electromagnetic field concept is defined as: a matter form of existence, distinct from substance (bodies), which can interact with substance, or it may also exist independently, and which is able to accumulate, transport and transfer energy, and which can exert ponderomotive actions on the bodies. • knowledge evolution regarding electric and magnetic phenomena encountered a significant delay with respect to other types of phenomena – mechanical, thermal, etc. • in contact with the surrounding reality, the man did not have the capacity to direct feel the electromagnetic nature phenomena (which cannot be seen, heard, touched, tasted or smelled). Their presence can be detected in an indirect way (for example through mechanical nature effects – forces, couples and others, generically called ponderomotive). • starting with XVIIIth century, the systematic approach of the magnetic and electric phenomena research began, by introducing the first coherent models and their interpretation theories.

4. ELECTROMAGNETIC FIELD THEORY Stages that reflected the human knowledge upon matter and the theories: The distance acting theory : some bodies exert instantaneous ponderomotive actions upon other bodies (with infinite transmission speed). The proximity theory (contiguity): interactions are not instantaneous, they are propagated with finite speed, step by step. The researches started by Faraday and continued by Maxwell for steady state media and by Hertz for moving media represent the fundamental classical macroscopic theory of electromagnetism. The microscopic theory: elaborated by Lorentz, extrapolated at microscopic scale the laws of Maxwell theory in vacuum (took into consideration discontinuous structure of the substance, but keeping the continuous repartition of the electromagnetic field). The relativistic theory: based on Einstein’s theory, who revised the classical mechanics concepts regarding the space and time when the bodies’ speed is close to the speed of light. Quantum theory : underlined that, when energy and impulse changed between particles are very small, one takes into consideration, beside the discontinuous structure of the substance, the discontinuous structure of electromagnetic field.

5. ELECTROMAGNETIC FIELD THEORY Chapter 1. Primitive and main derived quantities of macroscopic electromagnetic theory • presents the way in which the six primitive quantities are introduced and the way in which are defined the main derived quantities which characterize the electromagnetic field and the electromagnetic state of the bodies. 1.1 The coherent construction of a scientific theory. Physical model, physical quantities and attached mathematical relationships Aphysical system: is a well-defined assembly of matter existence forms (substance, field), having a certain internal structure and some forms of its interaction with the exterior. The physical model: is an idealization of the physical studied system and which is characterized by a set of physical quantities, correlated by a set of mathematical relations which describes this system from the phenomenological point of view. A physical quantity:a property of a physical system to be capable of quantitative evaluation.

6. ELECTROMAGNETIC FIELD THEORY 1.1 The coherent construction of a scientific theory. Physical model, physical quantities and attached mathematical relationships Physical quantities can be classified in many ways, by adopting various criteria. Below, we present only three of these criteria. I. Depending on the way in which they are introduced, there are: - primitive (primary) quantities (which are introduced directly, on the basis of experiments, by concrete indication of the measuring procedure) - derived quantities (which are introduced indirectly, by certain defining equations, in terms of previously known quantities). II. Function of the spatial domain to which they are associated: - local quantities (which are attached to each point in the space) -global quantities (which are associated to some volume, area or line domains). III. Function of the number of parameters which completely define them: - scalar quantities ( is enough to attach a single numerical value) -vector quantities (completely defined by specifying three parameters: magnitude, direction and sense) - tensor quantities (which are defined by an ordered scalar assembly).

7. ELECTROMAGNETIC FIELD THEORY 1.1 The coherent construction of a scientific theory. Physical model, physical quantities and attached mathematical relationships Between various physical quantities: certain mathematical relations which characterize the phenomena which take place in that system. Laws: mathematical relations, established on experimental basis, by abstraction, and which express the most general knowledge of the studied phenomena and they cannot be derived using logical analysis from other known relationships. In macroscopic theory of electromagnetic phenomena there are: - general laws which uses physical quantities and, eventually, universal constants, - material laws which contain as well constants specific to respective materials. From the point of view of cause-effect dependence: - state laws : contain physical quantities, but not their time derivatives - evolution laws: contain also time derivatives of some quantities. Theorems: can be deduced by logical analysis (they can be demonstrated) using other known relations (ultimately, by using the laws). Remark: the relative character of a relation to be considered law or theorem. The lower is the number of primitive quantities and laws used for theory, the more evolved is that theory (in the sense of its well organization).

8. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations Reviews some concepts and mathematical relationships absolutely indispensably for a substantial approach of the emf theory. Three-orthogonal coordinate systems - is a reference system defined by three surface families which intersect orthogonally. the scalar quantities, called coordinates, which intersect orthogonally line elements unit tangents of line elements area elements volume element

9. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations Cartesian system Cylindrical system Spherical system

10. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations Dot (scalar) product, cross (vector) product

11. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations. A few definitions related to vector fields The field line spectrum is a field line assembly from a certain area in the space. The flux tube is a tubular surface defined by the totality of the field lines which pass through all the points belonging to a small closed contour). Fig. 1

12. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations.Integrals Line integral of a vector field - a vector field - the unit tangent vector - the points where the vector field has the value - lengths of elementary line sub-domains (C) - open space curve

13. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations.Integrals Surface integral of a vector field - a vector field - the unit vector - the points where there is the value - elementary area sub-domains (S) – arbitrary oriented open surface

14. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations.Integrals Volume integral of a scalar field - a scalar field - the points where there is the value - elementary volume sub-domains (V) – a volume domain

15. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations. Space differential operators The differential operators: represent extremely important mathematical instruments when characterizing. the local behavior of scalar and vector fields. From these, only six are going to be presented, - three of them referring to continuity domains - and three to discontinuity surfaces. The divergence (div) is a differential operator applicable to vectors and it has as a result a scalar. The curl (curl) is a differential operator applicable to vectors and it has as a result a vector. The gradient (grad) is a differential operator applicable to scalars and it has as a result a vector.

16. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations. Space differential operators

17. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations. Space differential operators A surface which separates two media with different properties - normal unit vector in the point where we use the differential operators (from (1) to (2)) the values of the local quantities in the neighborhood of the separation surface between the two media

18. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations. Integral relationships

19. ELECTROMAGNETIC FIELD THEORY 1.2. Some mathematical considerations. Time derivative of a space integral