Note for ELECTROMAGNETIC THEORY AND TRANSMISSION LINE - ETTL By JNTU Heroes

Topics ( 5 )

Text from page-1

ELECTROMAGNETIC WAVES AND TRANSMISSION LINES UNIT-1 Electromagnetic theory is a prerequisite for a wide spectrum of studies in the field of Electrical Sciences and Physics. Electromagnetic theory can be thought of as generalization of circuit theory. There are certain situations that can be handled exclusively in terms of field theory. In electromagnetic theory, the quantities involved can be categorized as source quantities and field quantities. Source of electromagnetic field is electric charges: either at rest or in motion. However an electromagnetic field may cause a redistribution of charges that in turn change the field and hence the separation of cause and effect is not always visible. RF communication Microwave Engineering Antennas Electrical Machines Satellite Communication Atomic and nuclear research Radar Technology Remote sensing EMI EMC Quantum Electronics Introduction : Electromagnetic theory is a discipline concerned with the study of charges at rest and in motion. Electromagnetic principles are fundamental to the study of electrical engineering and physics. Electromagnetic theory is also indispensable to the understanding, analysis and design of various electrical, electromechanical and electronic systems. Some of the branches of study where electromagnetic principles find application are: Electric charge is a fundamental property of matter. Charge exist only in positive or negative integral multiple of electronic charge, -e, e= 1.60 × 10-19 coulombs. [It may be noted here that in 1962, Murray Gell-Mann hypothesized Quarks as the basic building

Text from page-2

blocks of matters. Quarks were predicted to carry a fraction of electronic charge and the existence of Quarks have been experimentally verified.] Principle of conservation of charge states that the total charge (algebraic sum of positive and negative charges) of an isolated system remains unchanged, though the charges may redistribute under the influence of electric field. Kirchhoff's Current Law (KCL) is an assertion of the conservative property of charges under the implicit assumption that there is no accumulation of charge at the junction. 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 a mathematical tool with which electromagnetic concepts are more conveniently expressed and best comprehended. Since use of vector analysis in the study of electromagnetic field theory results in real economy of time and thought, we first introduce the concept of vector analysis. Vector Analysis: The quantities that we deal in electromagnetic theory may be either scalar or vectors [There are other class of physical quantities called Tensors: where magnitude and direction vary with co ordinate axes]. Scalars are quantities characterized by magnitude only and algebraic sign. A quantity that has direction as well as magnitude is called a vector. Both scalar and vector quantities are function of time and position . A field is a function that specifies a particular quantity everywhere in a region. Depending upon the nature of the quantity under consideration, the field may be a vector or a scalar field. Example of scalar field is the electric potential in a region while electric or magnetic fields at any point is the example of vector field. A vector can be written as, , where, is the magnitude and unit vector which has unit magnitude and same direction as that of Two vector and are added together to give another vector is the . . 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

Text from page-3

Commutative Law..........................................(1.3) Associative Law.............................................(1.4) Distributive Law ............................................(1.5) The position vector = of a point P is the directed distance from the origin (O) to P, i.e., . Fig 1.3: Distance Vector If = OP and vector = OQ are the position vectors of the points P and Q then the distance Scaling of a vector is defined as , where is scaled version of vector scalar. Some important laws of vector algebra are: and is a 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)

Text from page-4

is unit vector perpendicular to and Fig 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) gives a scalar. Vector product (or cross product) gives a vector. The dot product between two vectors is defined as = |A||B|cosθAB ..................(1.6) Vector product is unit vector perpendicular to and Fig Fig 1.5 :Illustrating the left thumb rule for determining the vector cross product