A Review of Basic Electromagnetic Theories

Size: px
Start display at page:

Download "A Review of Basic Electromagnetic Theories"

Transcription

1 A Review of Basic Electromagnetic Theories Important Laws in Electromagnetics Coulomb s Law (1785) Gauss s Law (1839) Ampere s Law (1827) Ohm s Law (1827) Kirchhoff s Law (1845) Biot-Savart Law (1820) Faradays Law (1831) Maxwell Equations(1873) The governing equations of macroscopic electromagnetic phenomena. Predict the existence of electromagnetic waves. Predict light to be electromagnetic waves. Verification of electromagnetic waves: Hertz ( ) Radio communication: Marconi (1901) : Electric field intensity : Electric flux intensity : Magnetic field intensity : Magnetic flux intensity 1

2 ty Constituent relationship where : Permittivity : Permeability Continuity relationship : Electric current density : Magnetic current density : Volume electric charge density : Volume magnetic charge densi V a n Divergence Operator Physical meaning Divergence Theorem Curl Operator 2

3 Physical meaning Stoke s theorem: Integral Forms of Maxwell Equations a n S Power Relationship C From vector identity or for simply medium 3

4 or in integral form That is where : supplied energy : flow out energy : dissipated energy : stored electric and magnetic energy : total stored electric and magnetic energy in a closed surface.! Boundary Conditions 4

5 ! Time-Harmonic Fields Time-harmonic: : a real function in both space and time. : a real function in space. Thus all derivative of time becomes : a complex function in space. A phaser.. For a partial deferential equation all derivative of time can be replace with and all time dependence of can be removed and becomes a partial deferential equation of space only. Representing all field quantities as then the original Maxwell s equation becomes! Power Relationship 5

6 ! Poynting vector: Solution of Maxwell s Equations Vector Potential and Scalar Potential Since for simple media. Thus there exist a vector field such that is called vector potential. Then. Thus there exist a scalar potential such that 6

7 or Take the divergence of the above we have Since only the curl of is specified the divergence of can be arbitrarily chosen as. Then Also By applying vector identity we have The solutions are where. For time harmonic fields 7

8 and where is called the wave number and. The above equations are called nonhomogeneous Helmholtz s equations. Example: Let then HW#1 Prove that the wave functions for electric and magnetic fields in source free region are or On Wave in General A wave function can be specified in complex domain as below: 8

9 where : the magnitude real : the phase real. The corresponding time domain wave function is Equal phase surface are defined as Definitions: 1. Plane cylindrical or spherical waves: equal phase surfaces are planes cylinders or spheres. 2. Uniform waves: amplitude is constant over the equal phase surface. 3. Wave normal: surface normals of the equiphase surfaces. is the direction and is the curve along which the phase changes most rapidly. 4. Phase constant: the rate at which the phase decreases in some direction is called the phase constant in that direction (note: phase constant is not necessary a constant). Phase constant can be written in vector form as. The maximum phase constant is therefore. 5. Phase velocity: the speed the constant phase surface moves at in a given direction. The instantaneous equiphase surface of a wave is For ant increment the change in is To keep the phase constant for an incremental increase in time corresponding incremental change in is necessary. We have 9

10 . In cartesian coordinates The phase velocity along a wave normal is and is the smallest. Alternatively the wave function can be expressed as where is a complex function. A complex propagation constant can be defined as where is the vector phase constant and is the vector attenuation constant. 6. Wave impedance: the ratios of components of to. Follow right-hand cross-product rule of component rotated into. For example Example: 10

11 Plane Wave Propagation and Reflection From wave equation where free space wave number or propagation constant. In Cartesian coordinates considering the x component. Assume is independent of x and z then. The solutions are In time domain Constant phase 11

12 intrinsic impedance In general where Energy relations 12

13 Define velocity of propagation of energy as Then In general or Polarization In general If and then 1. Elliptically polarized: in general. 2. Linearly polarized:. 13

14 3. Circularly polarized: Ex: (RHC) No change in energy and power densities with time or space steady power flow. Plane Waves in Lossy Media If the material is conductive we have 14

15 Or if the material has dielectric loss with where is the attenuation constant the phase constant. Low-Loss Dielectrics: or and Good Conductor: and 15

16 Skin depth or depth of penetration: Meaning: plane wave decay be a factor of. At microwave frequencies is very small for a good conductor thus confined in a very thin layer of the conductor surface. 16

17 Oblique incidents Perpendicular Polarization (TE). The above fields must satisfy Boundary conditions which lead to 17

18 .. Note that the condition holds. If at (Brewster (polarization) angle) then Therefore or. No solution for. Snell s Law Definition of refraction index Total reflection occurs at critical angle. When is real. At angle larger than critical angle surface wave exists in dielectric. The wave decays inside the dielectric. For the propagation constant in media 2 becomes 18

19 Note that the minus sign is chosen such that the resulting field quantity in media 2 won t grow to infinity. In view of the phase term of the propagation wave in media 2 the wave decay in the media in direction. Parallel Polarization (TM) 19

20 ... Note that the condition holds. If at Brewster angle then. Therefore or. For nonmagnetic media Applications: Polarization separation anti-flare glasses 20

21 21

22 22

23 23

24 24

Chap. 1 Fundamental Concepts

Chap. 1 Fundamental Concepts NE 2 Chap. 1 Fundamental Concepts Important Laws in Electromagnetics Coulomb s Law (1785) Gauss s Law (1839) Ampere s Law (1827) Ohm s Law (1827) Kirchhoff s Law (1845) Biot-Savart Law (1820) Faradays

More information

UNIT I ELECTROSTATIC FIELDS

UNIT I ELECTROSTATIC FIELDS UNIT I ELECTROSTATIC FIELDS 1) Define electric potential and potential difference. 2) Name few applications of gauss law in electrostatics. 3) State point form of Ohm s Law. 4) State Divergence Theorem.

More information

CHAPTER 2. COULOMB S LAW AND ELECTRONIC FIELD INTENSITY. 2.3 Field Due to a Continuous Volume Charge Distribution

CHAPTER 2. COULOMB S LAW AND ELECTRONIC FIELD INTENSITY. 2.3 Field Due to a Continuous Volume Charge Distribution CONTENTS CHAPTER 1. VECTOR ANALYSIS 1. Scalars and Vectors 2. Vector Algebra 3. The Cartesian Coordinate System 4. Vector Cartesian Coordinate System 5. The Vector Field 6. The Dot Product 7. The Cross

More information

Electromagnetic Waves

Electromagnetic Waves Electromagnetic Waves Maxwell s equations predict the propagation of electromagnetic energy away from time-varying sources (current and charge) in the form of waves. Consider a linear, homogeneous, isotropic

More information

Electromagnetic Theory for Microwaves and Optoelectronics

Electromagnetic Theory for Microwaves and Optoelectronics Keqian Zhang Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Second Edition With 280 Figures and 13 Tables 4u Springer Basic Electromagnetic Theory 1 1.1 Maxwell's Equations 1 1.1.1

More information

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : ELECTROMAGNETIC FIELDS SUBJECT CODE : EC 2253 YEAR / SEMESTER : II / IV UNIT- I - STATIC ELECTRIC

More information

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad Electronics and Communicaton Engineering

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad Electronics and Communicaton Engineering INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 00 04 Electronics and Communicaton Engineering Question Bank Course Name : Electromagnetic Theory and Transmission Lines (EMTL) Course Code :

More information

Unit-1 Electrostatics-1

Unit-1 Electrostatics-1 1. Describe about Co-ordinate Systems. Co-ordinate Systems Unit-1 Electrostatics-1 In order to describe the spatial variations of the quantities, we require using appropriate coordinate system. A point

More information

Module 5 : Plane Waves at Media Interface. Lecture 36 : Reflection & Refraction from Dielectric Interface (Contd.) Objectives

Module 5 : Plane Waves at Media Interface. Lecture 36 : Reflection & Refraction from Dielectric Interface (Contd.) Objectives Objectives In this course you will learn the following Reflection and Refraction with Parallel Polarization. Reflection and Refraction for Normal Incidence. Lossy Media Interface. Reflection and Refraction

More information

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Content-ELECTRICITY AND MAGNETISM 1. Electrostatics (1-58) 1.1 Coulomb s Law and Superposition Principle 1.1.1 Electric field 1.2 Gauss s law 1.2.1 Field lines and Electric flux 1.2.2 Applications 1.3

More information

ELE3310: Basic ElectroMagnetic Theory

ELE3310: Basic ElectroMagnetic Theory A summary for the final examination EE Department The Chinese University of Hong Kong November 2008 Outline Mathematics 1 Mathematics Vectors and products Differential operators Integrals 2 Integral expressions

More information

Engineering Electromagnetics

Engineering Electromagnetics Nathan Ida Engineering Electromagnetics With 821 Illustrations Springer Contents Preface vu Vector Algebra 1 1.1 Introduction 1 1.2 Scalars and Vectors 2 1.3 Products of Vectors 13 1.4 Definition of Fields

More information

Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, ISBN:

Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, ISBN: MIT OpenCourseWare http://ocw.mit.edu Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. Please use the following

More information

DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY

DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY SIRUVACHUR-621113 ELECTRICAL AND ELECTRONICS DEPARTMENT 2 MARK QUESTIONS AND ANSWERS SUBJECT CODE: EE 6302 SUBJECT NAME: ELECTROMAGNETIC THEORY

More information

TECHNO INDIA BATANAGAR

TECHNO INDIA BATANAGAR TECHNO INDIA BATANAGAR ( DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING) QUESTION BANK- 2018 1.Vector Calculus Assistant Professor 9432183958.mukherjee@tib.edu.in 1. When the operator operates on

More information

444 Index Boundary condition at transmission line short circuit, 234 for normal component of B, 170, 180 for normal component of D, 169, 180 for tange

444 Index Boundary condition at transmission line short circuit, 234 for normal component of B, 170, 180 for normal component of D, 169, 180 for tange Index A. see Magnetic vector potential. Acceptor, 193 Addition of complex numbers, 19 of vectors, 3, 4 Admittance characteristic, 251 input, 211 line, 251 Ampere, definition of, 427 Ampere s circuital

More information

r r 1 r r 1 2 = q 1 p = qd and it points from the negative charge to the positive charge.

r r 1 r r 1 2 = q 1 p = qd and it points from the negative charge to the positive charge. MP204, Important Equations page 1 Below is a list of important equations that we meet in our study of Electromagnetism in the MP204 module. For your exam, you are expected to understand all of these, and

More information

ELECTROMAGNETISM. Second Edition. I. S. Grant W. R. Phillips. John Wiley & Sons. Department of Physics University of Manchester

ELECTROMAGNETISM. Second Edition. I. S. Grant W. R. Phillips. John Wiley & Sons. Department of Physics University of Manchester ELECTROMAGNETISM Second Edition I. S. Grant W. R. Phillips Department of Physics University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE Flow diagram inside front cover

More information

CHAPTER 9 ELECTROMAGNETIC WAVES

CHAPTER 9 ELECTROMAGNETIC WAVES CHAPTER 9 ELECTROMAGNETIC WAVES Outlines 1. Waves in one dimension 2. Electromagnetic Waves in Vacuum 3. Electromagnetic waves in Matter 4. Absorption and Dispersion 5. Guided Waves 2 Skip 9.1.1 and 9.1.2

More information

INTRODUCTION TO ELECTRODYNAMICS

INTRODUCTION TO ELECTRODYNAMICS INTRODUCTION TO ELECTRODYNAMICS Second Edition DAVID J. GRIFFITHS Department of Physics Reed College PRENTICE HALL, Englewood Cliffs, New Jersey 07632 CONTENTS Preface xi Advertisement 1 1 Vector Analysis

More information

DHANALAKSHMI SRINIVASAN COLLEGE OF ENGINEERING AND TECHNOLOGY

DHANALAKSHMI SRINIVASAN COLLEGE OF ENGINEERING AND TECHNOLOGY DHANALAKSHMI SRINIVASAN COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK III SEMESTER EE 8391 ELECTROMAGNETIC THEORY Regulation 2017 Academic Year

More information

ST.JOSEPH COLLEGE OF ENGINEERING,DEPARTMENT OF ECE

ST.JOSEPH COLLEGE OF ENGINEERING,DEPARTMENT OF ECE EC6403 -ELECTROMAGNETIC FIELDS CLASS/SEM: II ECE/IV SEM UNIT I - STATIC ELECTRIC FIELD Part A - Two Marks 1. Define scalar field? A field is a system in which a particular physical function has a value

More information

Electromagnetic Theory for Microwaves and Optoelectronics

Electromagnetic Theory for Microwaves and Optoelectronics Keqian Zhang Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Translated by authors With 259 Figures Springer Contents 1 Basic Electromagnetic Theory 1 1.1 Maxwell's Equations 1 1.1.1

More information

Describe the forces and torques exerted on an electric dipole in a field.

Describe the forces and torques exerted on an electric dipole in a field. Learning Outcomes - PHYS 2015 Electric charges and forces: Describe the electrical nature of matter; Explain how an object can be charged; Distinguish between electrical conductors and insulators and the

More information

Uniform Plane Waves Page 1. Uniform Plane Waves. 1 The Helmholtz Wave Equation

Uniform Plane Waves Page 1. Uniform Plane Waves. 1 The Helmholtz Wave Equation Uniform Plane Waves Page 1 Uniform Plane Waves 1 The Helmholtz Wave Equation Let s rewrite Maxwell s equations in terms of E and H exclusively. Let s assume the medium is lossless (σ = 0). Let s also assume

More information

INDEX rev..qxd 7/22/04 3:42 PM Page 425

INDEX rev..qxd 7/22/04 3:42 PM Page 425 INDEX rev..qxd 7/22/04 3:42 PM Page 425 I N D E X Admittance, 75 Air line, 43, 46 Ampere s circuital law, 202, 225 Amperian contour, 203 Angle azimuth, 109, 344 Brewster, 315 critical, 305 incidence, 303

More information

ELECTROMAGNETIC FIELDS AND WAVES

ELECTROMAGNETIC FIELDS AND WAVES ELECTROMAGNETIC FIELDS AND WAVES MAGDY F. ISKANDER Professor of Electrical Engineering University of Utah Englewood Cliffs, New Jersey 07632 CONTENTS PREFACE VECTOR ANALYSIS AND MAXWELL'S EQUATIONS IN

More information

VALLIAMMAI ENGINEERING COLLEGE

VALLIAMMAI ENGINEERING COLLEGE VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK III SEMESTER EE 8391 ELECTROMAGNETIC THEORY Regulation 2017 Academic

More information

Waves. Daniel S. Weile. ELEG 648 Waves. Department of Electrical and Computer Engineering University of Delaware. Plane Waves Reflection of Waves

Waves. Daniel S. Weile. ELEG 648 Waves. Department of Electrical and Computer Engineering University of Delaware. Plane Waves Reflection of Waves Waves Daniel S. Weile Department of Electrical and Computer Engineering University of Delaware ELEG 648 Waves Outline Outline Introduction Let s start by introducing simple solutions to Maxwell s equations

More information

UNIT-I Static Electric fields

UNIT-I Static Electric fields UNIT-I Static Electric fields In this chapter we will discuss on the followings: Coulomb's Law Electric Field & Electric Flux Density Gauss's Law with Application Electrostatic Potential, Equipotential

More information

EE6302 ELCTROMAGNETIC THEORY UNIT I ELECTROSTATICS I

EE6302 ELCTROMAGNETIC THEORY UNIT I ELECTROSTATICS I 13 EE630 ELCTROMAGNETIC THEORY UNIT I ELECTROSTATICS I 1. Define Scalar and Vector Scalar: Scalar is defined as a quantity that is characterized only by magnitude. Vector: Vector is defined as a quantity

More information

MUDRA PHYSICAL SCIENCES

MUDRA PHYSICAL SCIENCES MUDRA PHYSICAL SCIENCES VOLUME- PART B & C MODEL QUESTION BANK FOR THE TOPICS:. Electromagnetic Theory UNIT-I UNIT-II 7 4. Quantum Physics & Application UNIT-I 8 UNIT-II 97 (MCQs) Part B & C Vol- . Electromagnetic

More information

Chapter Three: Propagation of light waves

Chapter Three: Propagation of light waves Chapter Three Propagation of Light Waves CHAPTER OUTLINE 3.1 Maxwell s Equations 3.2 Physical Significance of Maxwell s Equations 3.3 Properties of Electromagnetic Waves 3.4 Constitutive Relations 3.5

More information

Electromagnetic Theory: PHAS3201, Winter 2008 Preliminaries D. R. Bowler drb/teaching.

Electromagnetic Theory: PHAS3201, Winter 2008 Preliminaries D. R. Bowler   drb/teaching. Electromagnetic Theory: PHA3201, Winter 2008 Preliminaries D. R. Bowler david.bowler@ucl.ac.uk http://www.cmmp.ucl.ac.uk/ drb/teaching.html 1 yllabus The course can be split into three main areas: electric

More information

Chapter 9. Electromagnetic waves

Chapter 9. Electromagnetic waves Chapter 9. lectromagnetic waves 9.1.1 The (classical or Mechanical) waves equation Given the initial shape of the string, what is the subsequent form, The displacement at point z, at the later time t,

More information

TENTATIVE CONTENTS OF THE COURSE # EE-271 ENGINEERING ELECTROMAGNETICS, FS-2012 (as of 09/13/12) Dr. Marina Y. Koledintseva

TENTATIVE CONTENTS OF THE COURSE # EE-271 ENGINEERING ELECTROMAGNETICS, FS-2012 (as of 09/13/12) Dr. Marina Y. Koledintseva TENTATIVE CONTENTS OF THE COURSE # EE-271 ENGINEERING ELECTROMAGNETICS, FS-2012 (as of 09/13/12) Dr. Marina Y. Koledintseva Part 1. Introduction Basic Physics and Mathematics for Electromagnetics. Lecture

More information

Electromagnetic Field Theory Chapter 9: Time-varying EM Fields

Electromagnetic Field Theory Chapter 9: Time-varying EM Fields Electromagnetic Field Theory Chapter 9: Time-varying EM Fields Faraday s law of induction We have learned that a constant current induces magnetic field and a constant charge (or a voltage) makes an electric

More information

ECE 4800 Fall 2011: Electromagnetic Fields and Waves. Credits: 4 Office Hours: M 6-7:30PM, Th 2-3:30, and by appointment

ECE 4800 Fall 2011: Electromagnetic Fields and Waves. Credits: 4 Office Hours: M 6-7:30PM, Th 2-3:30, and by appointment ECE 4800 Fall 2011: Electromagnetic Fields and Waves Instructor: Amar S. Basu Office: 3133 Engineering Email: abasu@eng.wayne.edu Phone: 313-577-3990 Lecture Times: M W 7:30PM - 9:20PM, Class Dates: 9/7/11

More information

Reflection/Refraction

Reflection/Refraction Reflection/Refraction Page Reflection/Refraction Boundary Conditions Interfaces between different media imposed special boundary conditions on Maxwell s equations. It is important to understand what restrictions

More information

1 Electromagnetic concepts useful for radar applications

1 Electromagnetic concepts useful for radar applications Electromagnetic concepts useful for radar applications The scattering of electromagnetic waves by precipitation particles and their propagation through precipitation media are of fundamental importance

More information

UNIT-I INTRODUCTION TO COORDINATE SYSTEMS AND VECTOR ALGEBRA

UNIT-I INTRODUCTION TO COORDINATE SYSTEMS AND VECTOR ALGEBRA SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : EMF(16EE214) Sem: II-B.Tech & II-Sem Course & Branch: B.Tech - EEE Year

More information

Session 8 Maxwell s Equations

Session 8 Maxwell s Equations Session 8 Maxwell s Equations Emma Bunce Physics Innovations Centre for Excellence in Learning and Teaching CETL (Leicester) Department of Physics and Astronomy University of Leicester 1 Contents Welcome...

More information

1 Chapter 8 Maxwell s Equations

1 Chapter 8 Maxwell s Equations Electromagnetic Waves ECEN 3410 Prof. Wagner Final Review Questions 1 Chapter 8 Maxwell s Equations 1. Describe the integral form of charge conservation within a volume V through a surface S, and give

More information

Acropolis Technical Campus, Indore, , (M.P.) Electronics and Communications Course Plan UG Electromagnetic Field Theory

Acropolis Technical Campus, Indore, , (M.P.) Electronics and Communications Course Plan UG Electromagnetic Field Theory Acropolis Technical Campus, Indore, 452020, (M.P.) Electronics and Communications Course Plan UG Electromagnetic Field Theory Course Code EC5001 Session: July- Dec 17 Semester:V Tutor Nisha Kiran Revision

More information

Maxwell s Equations & Hertz Waves

Maxwell s Equations & Hertz Waves Maxwell s Equations & Hertz Waves XI. Maxwell & Electromagnetic Waves A. Maxwell s Equations Dr. Bill Pezzaglia B. Hertz Waves & Poynting C. Polarization Updated: 3Aug5 A. Maxwell s Equations 3. Hints

More information

UNIVERSITY OF TORONTO Department of Electrical and Computer Engineering ECE320H1-F: Fields and Waves, Course Outline Fall 2013

UNIVERSITY OF TORONTO Department of Electrical and Computer Engineering ECE320H1-F: Fields and Waves, Course Outline Fall 2013 UNIVERSITY OF TORONTO Department of Electrical and Computer Engineering ECE320H1-F: Fields and Waves, Course Outline Fall 2013 Name Office Room Email Address Lecture Times Professor Mo Mojahedi SF2001D

More information

Part IB Electromagnetism

Part IB Electromagnetism Part IB Electromagnetism Theorems Based on lectures by D. Tong Notes taken by Dexter Chua Lent 2015 These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures.

More information

remain essentially unchanged for the case of time-varying fields, the remaining two

remain essentially unchanged for the case of time-varying fields, the remaining two Unit 2 Maxwell s Equations Time-Varying Form While the Gauss law forms for the static electric and steady magnetic field equations remain essentially unchanged for the case of time-varying fields, the

More information

General review: - a) Dot Product

General review: - a) Dot Product General review: - a) Dot Product If θ is the angle between the vectors a and b, then a b = a b cos θ NOTE: Two vectors a and b are orthogonal, if and only if a b = 0. Properties of the Dot Product If a,

More information

CHAPTER 7 ELECTRODYNAMICS

CHAPTER 7 ELECTRODYNAMICS CHAPTER 7 ELECTRODYNAMICS Outlines 1. Electromotive Force 2. Electromagnetic Induction 3. Maxwell s Equations Michael Faraday James C. Maxwell 2 Summary of Electrostatics and Magnetostatics ρ/ε This semester,

More information

Antennas and Propagation

Antennas and Propagation Antennas and Propagation Ranga Rodrigo University of Moratuwa October 20, 2008 Compiled based on Lectures of Prof. (Mrs.) Indra Dayawansa. Ranga Rodrigo (University of Moratuwa) Antennas and Propagation

More information

ELECTRICITY AND MAGNETISM

ELECTRICITY AND MAGNETISM ELECTRICITY AND MAGNETISM Chapter 1. Electric Fields 1.1 Introduction 1.2 Triboelectric Effect 1.3 Experiments with Pith Balls 1.4 Experiments with a Gold-leaf Electroscope 1.5 Coulomb s Law 1.6 Electric

More information

Chapter 1 Mathematical Foundations

Chapter 1 Mathematical Foundations Computational Electromagnetics; Chapter 1 1 Chapter 1 Mathematical Foundations 1.1 Maxwell s Equations Electromagnetic phenomena can be described by the electric field E, the electric induction D, the

More information

PHYS4210 Electromagnetic Theory Quiz 1 Feb 2010

PHYS4210 Electromagnetic Theory Quiz 1 Feb 2010 PHYS4210 Electromagnetic Theory Quiz 1 Feb 2010 1. An electric dipole is formed from two charges ±q separated by a distance b. For large distances r b from the dipole, the electric potential falls like

More information

ELECTRO MAGNETIC FIELDS

ELECTRO MAGNETIC FIELDS SET - 1 1. a) State and explain Gauss law in differential form and also list the limitations of Guess law. b) A square sheet defined by -2 x 2m, -2 y 2m lies in the = -2m plane. The charge density on the

More information

(Autonomous/ Affiliated to Anna University, Chennai) COIMBATORE DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

(Autonomous/ Affiliated to Anna University, Chennai) COIMBATORE DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING (Autonomous/ Affiliated to Anna University, Chennai) COIMBATORE-641 032 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING Semester III Academic Year: 2015-2016 Regulations 2014 COURSE PLAN Vision To

More information

1 Fundamentals of laser energy absorption

1 Fundamentals of laser energy absorption 1 Fundamentals of laser energy absorption 1.1 Classical electromagnetic-theory concepts 1.1.1 Electric and magnetic properties of materials Electric and magnetic fields can exert forces directly on atoms

More information

toroidal iron core compass switch battery secondary coil primary coil

toroidal iron core compass switch battery secondary coil primary coil Fundamental Laws of Electrostatics Integral form Differential form d l C S E 0 E 0 D d s V q ev dv D ε E D qev 1 Fundamental Laws of Magnetostatics Integral form Differential form C S dl S J d s B d s

More information

Classical Electrodynamics

Classical Electrodynamics Classical Electrodynamics Third Edition John David Jackson Professor Emeritus of Physics, University of California, Berkeley JOHN WILEY & SONS, INC. Contents Introduction and Survey 1 I.1 Maxwell Equations

More information

Engineering Electromagnetic Fields and Waves

Engineering Electromagnetic Fields and Waves CARL T. A. JOHNK Professor of Electrical Engineering University of Colorado, Boulder Engineering Electromagnetic Fields and Waves JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore CHAPTER

More information

UNIT-I Static Electric fields

UNIT-I Static Electric fields UNIT-I Static Electric fields In this chapter we will discuss on the followings: Coulomb's Law Electric Field & Electric Flux Density Gauss's Law with Application Electrostatic Potential, Equipotential

More information

cancel each other out. Thus, we only need to consider magnetic field produced by wire carrying current 2.

cancel each other out. Thus, we only need to consider magnetic field produced by wire carrying current 2. PC1143 2011/2012 Exam Solutions Question 1 a) Assumption: shells are conductors. Notes: the system given is a capacitor. Make use of spherical symmetry. Energy density, =. in this case means electric field

More information

Electricity & Magnetism Study Questions for the Spring 2018 Department Exam December 4, 2017

Electricity & Magnetism Study Questions for the Spring 2018 Department Exam December 4, 2017 Electricity & Magnetism Study Questions for the Spring 2018 Department Exam December 4, 2017 1. a. Find the capacitance of a spherical capacitor with inner radius l i and outer radius l 0 filled with dielectric

More information

we can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron.

we can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron. Physics II we can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron. Particle Symbol Charge (e) Mass (kg) Proton P +1 1.67

More information

ANNAI MATHAMMAL SHEELA ENGINEERING COLLEGE COURSE DELIVERY PLAN. Sub Code & Name: EE6302 & Electromagnetic Theory Year / Sem: II / IV

ANNAI MATHAMMAL SHEELA ENGINEERING COLLEGE COURSE DELIVERY PLAN. Sub Code & Name: EE6302 & Electromagnetic Theory Year / Sem: II / IV ANNAI MATHAMMAL SHEELA ENGINEERING COLLEGE COURSE DELIVERY PLAN Name of the Department: EEE Name of the Staff: Sub Code & Name: EE6302 & Electromagnetic Theory Year / Sem: II / IV 1 22.06.15 UNIT I ELECTROSTATICS

More information

Engineering Services Examination - UPSC ELECTRICAL ENGINEERING

Engineering Services Examination - UPSC ELECTRICAL ENGINEERING Engineering Services Examination - UPSC ELECTRICAL ENGINEERING Topic-wise Conventional Papers I & II 994 to 3 3 By Engineers Institute of India ALL RIGHTS RESERVED. No part of this work covered by the

More information

Antennas and Propagation. Chapter 2: Basic Electromagnetic Analysis

Antennas and Propagation. Chapter 2: Basic Electromagnetic Analysis Antennas and Propagation : Basic Electromagnetic Analysis Outline Vector Potentials, Wave Equation Far-field Radiation Duality/Reciprocity Transmission Lines Antennas and Propagation Slide 2 Antenna Theory

More information

University of Colorado at Boulder Summer 2017, Session B Tuesday, July 11 - Friday, August 11. Prof. Mik Sawicki PHYS 1120 COURSE CALENDAR WEEK 1

University of Colorado at Boulder Summer 2017, Session B Tuesday, July 11 - Friday, August 11. Prof. Mik Sawicki PHYS 1120 COURSE CALENDAR WEEK 1 University of Colorado at Boulder Summer 2017, Session B Tuesday, July 11 - Friday, August 11 1 T 07/11 Introduction and Electric charge 2 W 07/12 Coulomb s Law and Unit1 Electric Field. Unit 2 3 TH 07/13

More information

Radio Propagation Channels Exercise 2 with solutions. Polarization / Wave Vector

Radio Propagation Channels Exercise 2 with solutions. Polarization / Wave Vector /8 Polarization / Wave Vector Assume the following three magnetic fields of homogeneous, plane waves H (t) H A cos (ωt kz) e x H A sin (ωt kz) e y () H 2 (t) H A cos (ωt kz) e x + H A sin (ωt kz) e y (2)

More information

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/ Physics GRE: Electromagnetism G. J. Loges University of Rochester Dept. of Physics & stronomy xkcd.com/567/ c Gregory Loges, 206 Contents Electrostatics 2 Magnetostatics 2 3 Method of Images 3 4 Lorentz

More information

ECE357H1S ELECTROMAGNETIC FIELDS TERM TEST March 2016, 18:00 19:00. Examiner: Prof. Sean V. Hum

ECE357H1S ELECTROMAGNETIC FIELDS TERM TEST March 2016, 18:00 19:00. Examiner: Prof. Sean V. Hum UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING The Edward S. Rogers Sr. Department of Electrical and Computer Engineering ECE357H1S ELECTROMAGNETIC FIELDS TERM TEST 2 21 March 2016, 18:00

More information

Mansfield Independent School District AP Physics C: Electricity and Magnetism Year at a Glance

Mansfield Independent School District AP Physics C: Electricity and Magnetism Year at a Glance Mansfield Independent School District AP Physics C: Electricity and Magnetism Year at a Glance First Six-Weeks Second Six-Weeks Third Six-Weeks Lab safety Lab practices and ethical practices Math and Calculus

More information

Theory and Applications of Dielectric Materials Introduction

Theory and Applications of Dielectric Materials Introduction SERG Summer Seminar Series #11 Theory and Applications of Dielectric Materials Introduction Tzuyang Yu Associate Professor, Ph.D. Structural Engineering Research Group (SERG) Department of Civil and Environmental

More information

Problem set 3. Electromagnetic waves

Problem set 3. Electromagnetic waves Second Year Electromagnetism Michaelmas Term 2017 Caroline Terquem Problem set 3 Electromagnetic waves Problem 1: Poynting vector and resistance heating This problem is not about waves but is useful to

More information

COURTESY IARE. Code No: R R09 Set No. 2

COURTESY IARE. Code No: R R09 Set No. 2 Code No: R09220404 R09 Set No. 2 II B.Tech II Semester Examinations,APRIL 2011 ELECTRO MAGNETIC THEORY AND TRANSMISSION LINES Common to Electronics And Telematics, Electronics And Communication Engineering,

More information

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 00 0 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING : Electro Magnetic fields : A00 : II B. Tech I

More information

Antenna Theory (Engineering 9816) Course Notes. Winter 2016

Antenna Theory (Engineering 9816) Course Notes. Winter 2016 Antenna Theory (Engineering 9816) Course Notes Winter 2016 by E.W. Gill, Ph.D., P.Eng. Unit 1 Electromagnetics Review (Mostly) 1.1 Introduction Antennas act as transducers associated with the region of

More information

552 Electrodynamics-Fieldsand Waves

552 Electrodynamics-Fieldsand Waves 552 Electrodynamics-Fieldsand Waves so that Rd 1- R/d+l n (21) which when solved for Rid requires R 1 -, (22) d n -I PROBLEMS Section 7-1 1. For the following electric fields in a linear media of permittivity

More information

AP Physics C Electricity and Magnetism

AP Physics C Electricity and Magnetism AP Physics C Electricity and Magnetism Course overview This is a calculus based course in physics. The course is the equivalent of an introductory engineering course in Physics. The main objective of the

More information

Transmission Lines and E. M. Waves Prof. R. K. Shevgaonkar Department of Electrical Engineering Indian Institute of Technology, Bombay

Transmission Lines and E. M. Waves Prof. R. K. Shevgaonkar Department of Electrical Engineering Indian Institute of Technology, Bombay Transmission Lines and E. M. Waves Prof. R. K. Shevgaonkar Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture 18 Basic Laws of Electromagnetics We saw in the earlier lecture

More information

1 Fundamentals. 1.1 Overview. 1.2 Units: Physics 704 Spring 2018

1 Fundamentals. 1.1 Overview. 1.2 Units: Physics 704 Spring 2018 Physics 704 Spring 2018 1 Fundamentals 1.1 Overview The objective of this course is: to determine and fields in various physical systems and the forces and/or torques resulting from them. The domain of

More information

CONTENTS S.NO TOPIC PAGE NO. UNIT I ELECTROSTATICS I 1

CONTENTS S.NO TOPIC PAGE NO. UNIT I ELECTROSTATICS I 1 CONTENTS S.NO TOPIC PAGE NO. UNIT I ELECTROSTATICS I 1 1.1 Introduction to electrostatics 1 1.2 Sources and effects of electromagnetic fields 2 1.3 Divergence, Curl 7 1.4 Vector fields(dot, cross product)

More information

MIDSUMMER EXAMINATIONS 2001

MIDSUMMER EXAMINATIONS 2001 No. of Pages: 7 No. of Questions: 10 MIDSUMMER EXAMINATIONS 2001 Subject PHYSICS, PHYSICS WITH ASTROPHYSICS, PHYSICS WITH SPACE SCIENCE & TECHNOLOGY, PHYSICS WITH MEDICAL PHYSICS Title of Paper MODULE

More information

Introduction to Electromagnetic Theory

Introduction to Electromagnetic Theory Introduction to Electromagnetic Theory Lecture topics Laws of magnetism and electricity Meaning of Maxwell s equations Solution of Maxwell s equations Electromagnetic radiation: wave model James Clerk

More information

Physics 3312 Lecture 9 February 13, LAST TIME: Finished mirrors and aberrations, more on plane waves

Physics 3312 Lecture 9 February 13, LAST TIME: Finished mirrors and aberrations, more on plane waves Physics 331 Lecture 9 February 13, 019 LAST TIME: Finished mirrors and aberrations, more on plane waves Recall, Represents a plane wave having a propagation vector k that propagates in any direction with

More information

ELECTROMAGNETISM SUMMARY

ELECTROMAGNETISM SUMMARY Review of E and B ELECTROMAGNETISM SUMMARY (Rees Chapters 2 and 3) The electric field E is a vector function. E q o q If we place a second test charged q o in the electric field of the charge q, the two

More information

DEPARTMENT OF PHYSICS GOVT. V.Y.T. PG. AUTONOMOUS COLLEGE DURG

DEPARTMENT OF PHYSICS GOVT. V.Y.T. PG. AUTONOMOUS COLLEGE DURG DEPARTMENT OF PHYSICS GOVT. V.Y.T. PG. AUTONOMOUS COLLEGE DURG Approved syllabus for B.Sc. PHYSICS by the members of Board of Studies for the syllabus with the paper combinations is as under B.Sc.I: Paper

More information

EE 441: Advanced computer programming & Data Structures. L T P ESE: 100 Sessional 50 Laboratory: 50

EE 441: Advanced computer programming & Data Structures. L T P ESE: 100 Sessional 50 Laboratory: 50 EE 441: Advanced computer programming & Data Structures L T P 3-2 3 ESE: 100 Sessional 50 Laboratory: 50 1. Review of 1st semester IC course: Control structure, decision control structure, case control

More information

EET 492: Electromagnetic Fields and Waves. Fall Syllabus

EET 492: Electromagnetic Fields and Waves. Fall Syllabus EET 492: Electromagnetic Fields and Waves Fall 2007 Syllabus Lecturer Information: Name: Dr. Zhaoxian Zhou Office: TEC 326 Phone: (601)266 4482 Email: Zhaoxian.Zhou@usm.edu Web Page: www.usm.edu/zxzhou

More information

UNIT-III Maxwell's equations (Time varying fields)

UNIT-III Maxwell's equations (Time varying fields) UNIT-III Maxwell's equations (Time varying fields) Faraday s law, transformer emf &inconsistency of ampere s law Displacement current density Maxwell s equations in final form Maxwell s equations in word

More information

Here are some internet links to instructional and necessary background materials:

Here are some internet links to instructional and necessary background materials: The general areas covered by the University Physics course are subdivided into major categories. For each category, answer the conceptual questions in the form of a short paragraph. Although fewer topics

More information

Electromagnetic waves in free space

Electromagnetic waves in free space Waveguide notes 018 Electromagnetic waves in free space We start with Maxwell s equations for an LIH medum in the case that the source terms are both zero. = =0 =0 = = Take the curl of Faraday s law, then

More information

Electromagnetism. Christopher R Prior. ASTeC Intense Beams Group Rutherford Appleton Laboratory

Electromagnetism. Christopher R Prior. ASTeC Intense Beams Group Rutherford Appleton Laboratory lectromagnetism Christopher R Prior Fellow and Tutor in Mathematics Trinity College, Oxford ASTeC Intense Beams Group Rutherford Appleton Laboratory Contents Review of Maxwell s equations and Lorentz Force

More information

A Course Material on ELECTROMAGNETIC THEORY. Mr. P.MANIKANDAN ASSISTANT PROFESSOR DEPARTMENT OF ELECTRICAL AND ELCTRONICS ENGINEERING

A Course Material on ELECTROMAGNETIC THEORY. Mr. P.MANIKANDAN ASSISTANT PROFESSOR DEPARTMENT OF ELECTRICAL AND ELCTRONICS ENGINEERING EE6302 ELECTROMAGNETIC THEORY A Course Material on ELECTROMAGNETIC THEORY By Mr. P.MANIKANDAN ASSISTANT PROFESSOR DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING SASURIE COLLEGE OF ENGINEERING VIJAYAMANGALAM

More information

Syllabus of Physics for B. Sc. I For Academic Year Onward for Kumaun University in Uttarakhand

Syllabus of Physics for B. Sc. I For Academic Year Onward for Kumaun University in Uttarakhand Syllabus of Physics for B. Sc. I For Academic Year- 2014-15 Onward for Kumaun University in Uttarakhand I Paper: Mechanics and Properties of matter Maximum marks: 33 Note: This question paper consists

More information

ELECTRICITY AND MAGNETISM

ELECTRICITY AND MAGNETISM THIRD EDITION ELECTRICITY AND MAGNETISM EDWARD M. PURCELL DAVID J. MORIN Harvard University, Massachusetts Щ CAMBRIDGE Ell UNIVERSITY PRESS Preface to the third edition of Volume 2 XIII CONTENTS Preface

More information

Waves in Linear Optical Media

Waves in Linear Optical Media 1/53 Waves in Linear Optical Media Sergey A. Ponomarenko Dalhousie University c 2009 S. A. Ponomarenko Outline Plane waves in free space. Polarization. Plane waves in linear lossy media. Dispersion relations

More information

Light Scattering Group

Light Scattering Group Light Scattering Inversion Light Scattering Group A method of inverting the Mie light scattering equation of spherical homogeneous particles of real and complex argument is being investigated The aims

More information

EC2253 ELECTROMAGNETIC FIELDS

EC2253 ELECTROMAGNETIC FIELDS FATIMA MICHAEL COLLEGE OF ENGINEERIMG & TECHNOLOGY EC2253 ELECTROMAGNETIC FIELDS DEPT/ YEAR/ SEM: ECE/ II/ IV PREPARED BY: Mrs.K.Suganya/ Asst.Prof/ECE EC2253 ELECTROMAGNETIC FIELDS UNIT I STATIC ELECTRIC

More information

Plane Waves Part II. 1. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when

Plane Waves Part II. 1. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when Plane Waves Part II. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when (a) The angle of incidence is equal to the Brewster angle with E field perpendicular

More information