Engg Electromagnetics Lec01

Electromagnetics
Jornales, Pascual Lawrence B.
Electromagnetics
Course Outline:
Chapter 1: Vector Analysis
Chapter 2: Coulombs Law and Electric Field

Intensity
Chapter 3: Electric Flux Density, Gausss Law, and

Divergence
Chapter 4:Energy and Potential
Chapter 5: Conductors and Dielectrics
Chapter 6: Capacitance
Chapter 7: The Steady Magnetic Field
Electromagnetics
Course Outline:
Chapter 8: Magnetic Forces, Materials, and

Inductance
Chapter 9: Time-Varying Fields and Maxwells

Equations
Chapter 10:Transmission Lines
Chapter 11: The Uniform Plane Wave
Chapter 12: Plane Wave Reflection and Dispersion
Chapter 13: Guided Waves
Chapter 14: Electromagnetic Radiation and

Antennas
Electromagnetics
Chapter 1: Vector Analysis
Vector Analyis
It is a branch of mathematics concerned with

differentiation and integration of vector fields
Also called Vector Calculus
Electromagnetics
Chapter 1.1: Vector Analysis
Scalars
Vectors
- refers to a quantity
whose value may be
represented by a
single (+ or -) real
number
- refers to a quantity that

has both a magnitude*
and a direction in space
*note:
We adopt the convention that
magnitude infers absolute
value; the magnitude of any
quantity is, therefore, always
positive
Electromagnetics
Scalars
- refers to a quantity whose
value may be represented
by a single (+ or -) real
number
- some examples of scalars
include the mass, charge,
volume, time, speed,
temperature, or electric
potential at a point inside a
medium
The International System of

Units
Electromagnetics
Vectors
- refers to a quantity that
has both a magnitude
and a direction in space
- some examples of
scalars include the
displacement, velocity,
acceleration, and force
Electromagnetics
Electromagnetics
Chapter 1.2: Vector Algebra
Vector Addition
Follows the parallelogram law (tip-to-tail method)
Figure shows the sum of two vectors A and B.
Resultant Vector = A + B
These are coplanar vectors vector lying in a common

plane
Electromagnetics
Vector Addition
A+B=A+B
Electromagnetics
Vector Subtraction
A B = A + ( -B )
Electromagnetics
Vector Multiplication
- Vectors may be multiplied by scalars. The magnitude of the

vector changes, but its direction does not when the scalar
is positive, although it reverses direction when multiplied by
a negative scalar.
B
A
-r(B)
r(A)
-r(B)
r(A)
where r is 3
where -r is -3
Electromagnetics
Vector Division
- Multiplication by the reciprocal of that scalar
B
A
(B) / -r
(A) / r
(B) / -r
(A) / r
where r is 3
where -r is -3
Electromagnetics
Chapter 1.3: The Rectangular Coordinate System
To describe a vector accurately, some specific
lengths, directions, angles, projections, or
components must be given.
In the rectangular coordinate system we set up
three coordinate axes mutually at right angles to
each other and call them the x, y, and z axes.
A point is located by giving its x, y, and z
coordinates.
Electromagnetics
Electromagnetics
Electromagnetics
Electromagnetics
Video:
Algebra 11 - Cartesian Coordinates in Three
Dimensions.mp4
Electromagnetics
Chapter 1.4: Vector Components and Unit Vector
To describe a vector in the
rectangular coordinate
system,let us first consider a
vector r extending outward
from the origin.
A logical way to identify this
vector is by giving the three
component vectors, lying
along the three coordinate
axes, whose vector sum
must be the given vector.
Electromagnetics
The component vectors have magnitudes
that depend on the given vector (such as
r), but they each have a known and
constant direction.
This suggests the use of unit vectors
having unit magnitude by definition;
these are parallel to the coordinate
axes and they point in the direction of
increasing coordinate values.
We reserve the symbol a for a unit vector
and identify its direction by an appropriate
subscript.
Thus ax ,a y ,and a z are the unit vectors in
the rectangular coordinate system.
They are directed along the x, y, and z
axes, respectively, as shown in the figure.
Electromagnetics
rP = 1ax + 2ay + 3az
rQ = 2ax + -2ay + 1az
RPQ = rQ-rP
RPQ = ( 2-1 )ax + ( -2-2 )ay + ( 1-3 )az
RPQ = ax + -4ay -2az
Electromagnetics
Electromagnetics
Chapter 1.5: The Vector Field
It is a function of a space whose value at
each point is a vector quantity. A vector
field is like a scalar field, only for vectors.
We have defined a vector field as a vector
function of a position vector. In general, the
magnitude and direction of the function will
change as we move throughout the region,
and the value of the vector function must
be determined using the coordinate values
of the point in question.
Because we have considered only the
rectangular coordinate system, we expect
the vector to be a function of the variables
x, y, and z.
If we again represent the position vector as r,
then a vector field G can be expressed in
functional notation as G(r); a scalar field T
is written as T(r).
Electromagnetics
Chapter 1.5: The Vector Field
Drawing Vector Field:
Vector fields, introduction Multivariable calculus
Khan Academy.mp4
Vector Field in Electromagnetics:
Vector Field.mp4
Electromagnetics
Chapter 1.6: The Dot Product
Electromagnetics
Chapter 1.6: The Dot Product
Electromagnetics
Chapter 1.7: The Cross Product
Electromagnetics
Electromagnetics
Electromagnetics
Electromagnetics
Cross Product and Dot Product Visual explanation.mp4
Electromagnetics
Chapter 1.8: Other Coordinate Systems: Circular
Cylindrical Coordinates
Electromagnetics
Chapter 1.8: Other Coordinate Systems: Circular Cylindrical Coordinates
Electromagnetics
Electromagnetics
Physics - Advanced E&M Ch 1 Math Concepts (25 of

55) Cylindrical CoordinatesPoint and Unit Vectors.mp4
Electromagnetics
Chapter 1.9: Other Coordinate Systems:
Spherical Coordinate
A spherical coordinate system is a
coordinate system for threedimensional space where the
position of a point is specified by
three numbers:
-the radial distance of that point from
a fixed origin,
-its polar angle measured from a
fixed zenith direction,
-and the azimuth angle of its
orthogonal projection on a reference
plane that passes through the origin
and is orthogonal to the zenith,
measured from a fixed reference
direction on that plane.
Electromagnetics
Chapter 1.9: Other Coordinate Systems: Spherical Coordinate
Electromagnetics
Chapter 1.9: Other Coordinate Systems: Spherical Coordinate
Electromagnetics
Chapter 1.9: Other Coordinate Systems: Spherical Coordinatet
Converting from Cartesian (x,y,z) to Spherical (,,).mp4
Thank You!

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Electromagnetics

Jornales, Pascual Lawrence B.

Chapter 1: Vector Analysis

Chapter 2: Coulombs Law and Electric Field

Chapter 3: Electric Flux Density, Gausss Law, and

Chapter 4:Energy and Potential

Chapter 5: Conductors and Dielectrics

Chapter 7: The Steady Magnetic Field

Chapter 8: Magnetic Forces, Materials, and

Chapter 9: Time-Varying Fields and Maxwells

Chapter 10:Transmission Lines

Chapter 11: The Uniform Plane Wave

Chapter 12: Plane Wave Reflection and Dispersion

Chapter 13: Guided Waves

Chapter 14: Electromagnetic Radiation and

It is a branch of mathematics concerned with

Also called Vector Calculus

- refers to a quantity that

The International System of

Follows the parallelogram law (tip-to-tail method)

Figure shows the sum of two vectors A and B.

These are coplanar vectors vector lying in a common

- Vectors may be multiplied by scalars. The magnitude of the

- Multiplication by the reciprocal of that scalar

rP = 1ax + 2ay + 3az

rQ = 2ax + -2ay + 1az

Cross Product and Dot Product Visual explanation.mp4

Physics - Advanced E&M Ch 1 Math Concepts (25 of

Converting from Cartesian (x,y,z) to Spherical (,,).mp4

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