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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY
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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

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

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)

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

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