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Electromagnetic Theory

by Vssut RulersVssut Rulers
Type: NoteInstitute: Veer Surendra Sai University Of Technology VSSUT Course: B.Tech Specialization: Electrical EngineeringOffline Downloads: 23Views: 1011Uploaded: 3 months ago

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Vssut Rulers
Vssut Rulers
Veer Surendra Sai University of Technology, Orissa, Burla, India Department of Electrical Engineering, Syllabus of Bachelor of Technology in Electrical Engineering, 2010 (6TH SEMESTER) ELECTROMAGNETIC THEORY (3-1-0) MODULE-I (10 HOURS) Representation of vectors in Cartesian, Cylindrical and Spherical coordinate system, Vector products, Coordinate transformation. The Law of force between elementary electric Charges, Electric Field Intensity and Potential due to various charge configuration, Electric Flux density, Gauss law and its application, Application of Gauss Law to differential Volume element, Divergence Theorem. Potential Gradient, Dipole, and Energy Density in Electrostatic Field. MODULE-II (10 HOURS) Current and Conductors, Continuity of Current, Conductor Properties and Boundary Conditions. The Method of Images, Nature of dielectric Materials, Boundary Conditions for Perfect Dielectric Materials Capacitance, Poisson’s & Laplace equation, Uniqueness Theorem, Analytical Solution in one dimension.Use of MATLAB Steady Magnetic Field: Biot Savart Law, Ampere’s Circuital Law, Stoke’s Theorem, Scalar and Vector Magnetic Potential, MODULE-III (10 HOURS) Force on a moving Charge, Force on a differential Current Element, Force & Torque Magnetisation & Permeability, Magnetic Boundary Conditions, Inductance & Mutual Inductance. Time Varying Fields: Faraday’s Law, Displacement Current, Maxwell’s Equation. MODULE-IV (10 HOURS) Wave propagation in Free Space, Dielectric, and Good Conductor. Poynting’s Theorem and wave power, Wave polarization, Reflection and Transmission of Uniform Plane Waves at Normal & Oblique incidence, Standing Wave Ratio, Basic Wave Guide Operation and Basic Antenna Principles. BOOKS [1]. W. H. Hayt (Jr ), J. A. Buck, “Engineering Electromagnetics”, TMH [2]. K. E. Lonngren, S.V. Savor, “Fundamentals of Electromagnetics with Matlab”, PHI [3]. E.C.Jordan, K.G. Balmain, “Electromagnetic Waves & Radiating System”, PHI. [4]. M. N. Sadiku, “Elements of Electromagnetics”, Oxford University Press.
MODULE-I INTRODUCTION: Electromagnetic theory is concerned with the study of charges at rest and in motion. Electromagnetic principles are fundamental to the study of electrical engineering. Electromagnetic theory is also required for the understanding, analysis and design of various electrical, electromechanical and electronic systems. Electromagnetic theory can be thought of as generalization of circuit theory. Electromagnetic theory deals directly with the electric and magnetic field vectors where as circuit theory deals with the voltages and currents. Voltages and currents are integrated effects of electric and magnetic fields respectively. Electromagnetic field problems involve three space variables along with the time variable and hence the solution tends to become correspondingly complex. Vector analysis is the required mathematical tool with which electromagnetic concepts can be conveniently expressed and best comprehended. Since use of vector analysis in the study of electromagnetic field theory is prerequisite, first we will go through vector algebra. Applications of Electromagnetic theory: This subject basically consist of static electric fields, static magnetic fields, time-varying fields & it’s applications. One of the most common applications of electrostatic fields is the deflection of a charged particle such as an electron or proton in order to control it’s trajectory. The deflection is achieved by maintaining a potential difference between a pair of parallel plates. This principle is used in CROs, ink-jet printer etc. Electrostatic fields are also used for sorting of minerals for example in ore separation. Other applications are in electrostatic generator and electrostatic voltmeter. The most common applications of static magnetic fields are in dc machines. Other applications include magnetic deflection, magnetic separator, cyclotron, hall effect sensors, magneto hydrodynamic generator etc. Vector Analysis: The quantities that we deal in electromagnetic theory may be either scalar or vectors. Scalars are quantities characterized by magnitude only. A quantity that has direction as well as magnitude is called a vector. In electromagnetic theory both scalar and vector quantities are function of time and position. A vector can be written as, , where, is the magnitude and which has unit magnitude and same direction as that of Two vector and is the unit vector . are added together to give another vector . We have ................(1.1) Let us see the animations in the next pages for the addition of two vectors, which has two rules:
1: Parallelogram law and 2: Head & tail rule Scaling of a vector is defined as , where Some important laws of vector algebra are: is scaled version of vector and is a scalar. Commutative Law..........................................(1.3) Associative Law.............................................(1.4) Distributive Law ............................................(1.5) The position vector If = OP and of a point P is the directed distance from the origin (O) to P, i.e., = . = OQ are the position vectors of the points P and Q then the distance vector Fig 1.3: Distance Vector Product of Vectors When two vectors and are multiplied, the result is either a scalar or a vector depending how the two vectors were multiplied. The two types of vector multiplication are: Scalar product (or dot product) Vector product (or cross product) gives a scalar. gives a vector. The dot product between two vectors is defined as Vector product = |A||B|cosθAB ..................(1.6)
is unit vector perpendicular to and Fig 1.4 : Vector dot product The dot product is commutative i.e., Associative law does not apply to scalar product. The vector or cross product of two vectors perpendicular to the plane containing given by right hand rule. and and and distributive i.e., is denoted by . . is a vector , the magnitude is given by and direction is ............................................................................................(1.7) where is the unit vector given by, . The following relations hold for vector product. = i.e., cross product is non commutative ..........(1.8) i.e., cross product is distributive.......................(1.9) i.e., cross product is non associative..............(1.10) Scalar and vector triple product : Scalar triple product Vector triple product .................................(1.11) ...................................(1.12)

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