Dr. G. V. Nagesh KumarProfessor and Head, Department of EEE,

JNTUA College of Engineering Pulivendula

“Our thoughts and feelings have

electromagnetic reality.

Manifest wisely.”

Electromagnetic Field Theory

Lecture 1

Syllabus / Lectures

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1. Vector Analysis, Coulomb’s Law, Electric Field Intensity

2. Electric Flux Density, Gauss’s Law, Divergence

3. Electric Potential, Effect of dielectric medium, Capacitance

4. Biot Savart’s law, Ampere’s law, Curl

5. MMF, Reluctance, Magnetic circuits, Self and Mutual

inductance of simple configurations.

6. Lorentz force, Faraday’s law

Weightage

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EMT: Should I Study or Leave This Subject for GATE Exam?

• This subject accounts for approximately 4-6 marks

Electromagnetics finds a number of applications in various streams of Electrical engineering, some are

The laws that are studied here are so fundamental that even Network Analysis laws have been derived from

here. So, if you do not understand the laws of Electromagnetism then you lack the thorough knowledge of

Electrical Engineering.

Power Systems is another subject where combined application of Electromagnetic theory and Network theory

can help prepare, understand and score well in the subject.

Also, understanding the operation of Electrical Machines, Transformers which is an important subject for GATE

is impossible without the understanding of the laws of Electromagnetism.

Electromagnetics is generally considered a tough subject since most of the students are unable to comprehend and

understand it during their graduation days.

Preparation Strategies

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• Understanding the physical interpretations of Electromagnetism basics, by Visualization And

Imagination beyond the mathematics that is involved, develop enhanced understanding of

Electromagnetics.

• It is necessary to cover all the topics of the subject while preparing since all of them are Highly inter-

linked.

• Need a proper and complete understanding of Coordinate systems.

• Since formulae for all the three coordinate systems are very important and find repeated application

throughout the subject, apart from the questions that are put up directly from these topics, it is highly

advisable to Remember these formulae.

• You can take help of micro notes, make Formulae Sheet and revise it often to remember them.

• It’s easy to concentrate on either speed or accuracy at once but what GATE exam demands is

Concentration on accuracy in a stipulated time.

Introduction

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• Electromagnetics is the study of the effect of charges at rest and charges in motion.

Some special cases of electromagnetics:

Electrostatics: charges at rest

Magnetostatics: charges in steady motion (DC)

Electromagnetic : charges in time-varying motion (AC)

• Fundamental vector field quantities in electromagnetics:

Electric field intensity - E

units = volts per meter (V/m )

Electric flux density (electric displacement) - D

units = coulombs per square meter (C/m2)

Magnetic field intensity - H

units = amps per meter (A/m)

Magnetic flux density- B

units = teslas = webers per square meter (T = Wb/ m2 )

Introduction

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• transmitter and receiverare connected by a “field.”

• When an event in one place has an effect on

something at a different location, we talk

about the events as being connected by a

“field”.

• A field is a spatial distribution of a quantity;

in general, it can be either scalar or vector in

nature.

Scalar and Vector

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Unit Vector / Direction Vector

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A unit vector is a vector with a magnitude of one unit.

Any vector can be expressed as a scalar multiple of its unit vector.

Position Vector

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Distance Vector

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Coordinate Systems

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• Coordinates systems are often used to specify the position of apoint, but they may also be used to specify the position of morecomplex figures such as lines, planes, circles or spheres.

• The choice of the coordinate system is based on the problemone is studying.

• Certain problems are solved easily by using rectangularcoordinate systems whereas certain others are not.

• Some coordinate systems make more sense, make it easier todescribe a system.

• Coordinates give you a systematic way of naming the points in aspace.

Coordinate Systems

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• Consider the set of locations in your room. Each point has a uniqueidentity, but they don’t come with names.

• We can use descriptions, like “the point at the corner of the desk”,or “the set of points exactly three inches from the top of the lamp”,but that sort of thing is ad hoc. If we can name themsystematically, we can start reasoning about the whole space.

• A simple way to systematically name every point, called aCartesian coordinate system, is to give its perpendicular distancefrom the floor and two adjacent walls—each point gets a uniquename in this system.

• If the room is circular, you’d have to make an imaginary wall, or youcould use the height from the floor, the distance from the center,and the angle between a line from the center through the point anda line from the center through another fixed point, like the door.This is an example of cylindrical coordinates.

• On the globe, we systematically name locations by giving theirlatitude, longitude, and altitude. you’re using a spherical coordinateplane in real life.

Cartesian System

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Ranges

Cartesian System

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Cartesian System

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Cylindrical System

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Cylindrical System

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Cylindrical System

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Cylindrical System

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Cylindrical System

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Relation between Cartesian and Cylindrical

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Spherical System

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Spherical System

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Spherical System

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Spherical System

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Spherical System

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Spherical System

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Spherical System

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Relation between Cartesian and Spherical System

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Vector Multiplication

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The Knowledge of vector multiplication allows us to transform the vectors from one coordinate system to other.

Scalar Product or DOT Product

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Properties of DOT Product

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Applications of DOT Product

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Applications of DOT Product

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Vector Product or Cross Product

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Vector Product or Cross Product

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Vector Product or Cross Product

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Applications of Cross Product

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Vector Product or Cross Product

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Vector Product or Cross Product

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Transformation of Vectors

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Cartesian to Cylindrical

Transformation of Vectors

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Transformation of Vectors

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Transformation of Vectors

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Coulomb's Law

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Coulomb's Law

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Coulomb's Law

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Coulomb's Law

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Vector form of Coulomb's Law

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Vector form of Coulomb's Law

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Force due to 'n' Charges

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Coulomb's Law : Steps to solve Problems

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Electric Field Intensity

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An electric field is an elegant way of characterising the electrical environment of a system of charges.

Electric Field Intensity

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Electric Field Intensity

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Electric Field Intensity

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Electric Field Intensity : Units

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Electric Field Intensity : n Charges

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Electric Field Intensity : Observations

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Charge Configurations

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Charge Configurations

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E due to Infinite Line Charge

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E due to Infinite Line Charge

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E due to Charged Circular Ring

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E due to Charged Circular Ring

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E due to Infinite Sheet of Charge

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E due to various Configurations

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Thank youEmail: nagesh.eee@jntua.ac.in