Maxwell Equations: Electromagnetic Waves
|
|
- Beverly McCoy
- 6 years ago
- Views:
Transcription
1 Maxwell Equations: Electromagnetic Waves Maxwell s Equations contain the wave equation The velocity of electromagnetic waves: c = x 10 8 m/s The relationship between E and B in an EM wave Energy in EM waves: the Poynting vector x z y 1
2 The equations so far... Gauss Law for E Fields Gauss Law for B Fields Faraday s Law Ampere s Law 2
3 A problem with Ampere s Law Consider a wire and a capacitor. C is a loop. Time dependent situation: current flows in the wire as the capacitor charges up or down. 3
4 Maxwell s Displacement Current, I d 4
5 Calculating Displacement Current Consider a parallel plate capacitor with circular plates of radius R. If charge is flowing onto one plate and off the other plate at a rate I = dq/dt what is I d? The displacement current is not a current. It represents magnetic fields generated by time varying electric fields. 5
6 Calculating the B field Example 6
7 Maxwell s Equations (1865) in Systeme International (SI or mks) units7
8 Maxwell s Equations (Free Space) Note the symmetry of Maxwell s Equations in free space, when no charges or currents are present We can predict the existence of electromagnetic waves. Why? Because the wave equation is contained in these equations. Remember the wave equation. h is the variable that is changing in space (x) and time (t). v is the velocity of the wave. 8
9 Review of Waves from Mechanics The one-dimensional wave equation: has a general solution of the form: A solution for waves traveling in the +x direction is: 9
10 Four Step Plane Wave Derivation Step 1 Assume we have a plane wave propagating in z (i.e. E, B not functions of x or y) Example: Step 2 Apply Faraday s Law to infinitesimal loop in x-z plane x E x E x x y B y z 1 z 2 Z z 10
11 Four Step Plane Wave Derivation Step 3 Apply Ampere s Law to an infinitesimal loop in the y-z plane: x E x Z y B y z 1 z 2 B y y z Step 4: Use results from steps 2 and 3 to eliminate B y 11
12 Velocity of Electromagnetic Waves We derived the wave equation for E x : The velocity of electromagnetic waves in free space is: Putting in the measured values for µ 0 & ε 0, we get: This value is identical to the measured speed of light! We identify light as an electromagnetic wave. 12
13 Electromagnetic Spectrum ~1850: infrared, visible, and ultraviolet light were the only forms of electromagnetic waves known. Visible light (human eye) 13
14 Electromagnetic Spectrum 14
15 Sunscreen Absorbs UV _Vis_Sunscreen.jpg/800px-UV_and_Vis_Sunscreen.jpg 15
16 What a Bee Sees: 16
17 Wien s Displacement Law 17
18 How is B related to E? We derived the wave equation for E x : We could have derived for B y : How are E x and B y related in phase and magnitude? Consider the harmonic solution: where 18
19 E & B in Electromagnetic Waves Plane Wave: where: x z y The direction of propagation is given by the cross product where are the unit vectors in the (E,B) directions. Nothing special about (E x,b y ); eg could have (E y, -B x ) Note cyclical relation: 19
20 Energy in Electromagnetic Waves Electromagnetic waves contain energy. We know the energy density stored in E and B fields: In an EM wave, B = E/c u B = 1 E = 1 ε E = u c µ 0 2 The total energy density in an EM wave = u, where 2 E The Intensity of a wave is defined as the average power (P av =u av /Δt) transmitted per unit area = average energy density times wave velocity: For ease in calculation define Z 0 as: 20
21 The Poynting Vector The direction of the propagation of the electromagnetic wave is given by: This energy transport is defined by the Poynting vector S as: S has the direction of propagation of the wave The magnitude of S is directly related to the energy being transported by the wave The intensity for harmonic waves is then given by: 21
22 Characteristics z x S 22
23 Summary of Electromagnetic Radiation combined Faraday s Law and Ampere s Law time varying B-field induces E-field time varying E-field induces B-field E-field and B-field are perpendicular energy density Poynting Vector describes power flow E units: watts/m 2 B S 23
Maxwell s Equations & Electromagnetic Waves. The Equations So Far...
Maxwell s Equations & Electromagnetic Waves Maxwell s equations contain the wave equation Velocity of electromagnetic waves c = 2.99792458 x 1 8 m/s Relationship between E and B in an EM wave Energy in
More informationThe equations so far... Gauss Law for E Fields. Gauss Law for B Fields. B da. inside. d dt. n C 3/28/2018
The equations so far... Gauss Law for E Fields E da S n 1 Q inside Gauss Law for B Fields B da S n C Faraday s Law d E dl dt S B da n Ampere s Law B dl I C 3/8/18 1 Ampere s Law B dl I inside _ path No
More informationElectricity & Optics
Physics 24100 Electricity & Optics Lecture 21 Chapter 30 sec. 1-4 Fall 2012 Semester Matthew Jones Question An LC circuit has =100 and =100. If it oscillates with an amplitude of 100 mv, what is the amplitude
More informationAlong with C1 the magnetic field is also observed at location C 2 though no current is threading through this loop.
Displacement current British physicist James C. Maxwell gave final shape to all phenomenon connecting electricity and magnetism. He noticed an inconsistency in Ampere s Law connecting Electric current
More informationEM Waves. From previous Lecture. This Lecture More on EM waves EM spectrum Polarization. Displacement currents Maxwell s equations EM Waves
EM Waves This Lecture More on EM waves EM spectrum Polarization From previous Lecture Displacement currents Maxwell s equations EM Waves 1 Reminders on waves Traveling waves on a string along x obey the
More informationChapter 31 Maxwell s Equations and Electromagnetic Waves. Copyright 2009 Pearson Education, Inc.
Chapter 31 Maxwell s Equations and Electromagnetic Waves Units of Chapter 31 Changing Electric Fields Produce Magnetic Fields; Ampère s Law and Displacement Current Gauss s Law for Magnetism Maxwell s
More informationPHYS 1444 Section 004 Lecture #22
PHYS 1444 Section 004 Lecture #22 Monday, April 23, 2012 Dr. Extension of Ampere s Law Gauss Law of Magnetism Maxwell s Equations Production of Electromagnetic Waves Today s homework is #13, due 10pm,
More informationChapter 31 Maxwell s Equations and Electromagnetic Waves. Copyright 2009 Pearson Education, Inc.
Chapter 31 Maxwell s Equations and Electromagnetic Waves Units of Chapter 31 Changing Electric Fields Produce Magnetic Fields; Ampère s Law and Displacement Current Gauss s Law for Magnetism Maxwell s
More informationW15D1: Poynting Vector and Energy Flow. Today s Readings: Course Notes: Sections 13.6,
W15D1: Poynting Vector and Energy Flow Today s Readings: Course Notes: Sections 13.6, 13.12.3-13.12.4 1 Announcements Final Math Review Week 15 Tues from 9-11 pm in 32-082 Final Exam Monday Morning May
More informationProblem Solving 9: Displacement Current, Poynting Vector and Energy Flow
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Problem Solving 9: Displacement Current, Poynting Vector and Energy Flow Section Table and Group Names Hand in one copy per group at the end
More informationChapter 29: Maxwell s Equation and EM Waves. Slide 29-1
Chapter 29: Maxwell s Equation and EM Waves Slide 29-1 Equations of electromagnetism: a review We ve now seen the four fundamental equations of electromagnetism, here listed together for the first time.
More informationLecture 35. PHYC 161 Fall 2016
Lecture 35 PHYC 161 Fall 2016 Induced electric fields A long, thin solenoid is encircled by a circular conducting loop. Electric field in the loop is what must drive the current. When the solenoid current
More informationε induced Review: Self-inductance 20.7 RL Circuits Review: Self-inductance B induced Announcements
Announcements WebAssign HW Set 7 due this Friday Problems cover material from Chapters 20 and 21 We re skipping Sections 21.1-21.7 (alternating current circuits) Review: Self-inductance induced ε induced
More informationPhysics 1502: Lecture 25 Today s Agenda
Physics 1502: Lecture 25 Today s Agenda Announcements: Midterm 2: NOT Nov. 6 Following week Homework 07: due Friday net week AC current esonances Electromagnetic Waves Mawell s Equations - evised Energy
More informationKINGS 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 informationELECTRO 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 informationW13D2: Displacement Current, Maxwell s Equations, Wave Equations. Today s Reading Course Notes: Sections
W13D2: Displacement Current, Maxwell s Equations, Wave Equations Today s Reading Course Notes: ections 13.1-13.4 1 Announcements Math Review Tuesday May 6 from 9 pm-11 pm in 26-152 Pset 10 due May 6 at
More informationE or B? It Depends on Your Perspective
E or B? It Depends on Your Perspective Alec sees a moving charge, and he knows that this creates a magnetic field. From Brittney s perspective, the charge is at rest, so the magnetic field is zero. Is
More informationChapter 31. Faraday s Law
Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field B s II I d d μ o d μo με o o E ds E B Induction A loop of wire is connected to a sensitive ammeter
More informationElectromagnetic Waves
Lecture 20 Chapter 34 Physics II Electromagnetic Waves Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Let s finish climbing our EM mountain. Maxwell s equations Let s revisit
More informationSlide 1 / 24. Electromagnetic Induction 2011 by Bryan Pflueger
Slide 1 / 24 Electromagnetic Induction 2011 by Bryan Pflueger Slide 2 / 24 Induced Currents If we have a galvanometer attached to a coil of wire we can induce a current simply by changing the magnetic
More informationLecture 36: WED 18 NOV CH32: Maxwell s Equations I
Physics 2113 Jonathan Dowling Lecture 36: WED 18 NOV H32: Maxwell s Equations I James lerk Maxwell (1831-1879) Maxwell I: Gauss Law for E-Fields: charges produce electric fields, field lines start and
More informationBasics of Electromagnetics Maxwell s Equations (Part - I)
Basics of Electromagnetics Maxwell s Equations (Part - I) Soln. 1. C A. dl = C. d S [GATE 1994: 1 Mark] A. dl = A. da using Stoke s Theorem = S A. ds 2. The electric field strength at distant point, P,
More informationAnnouncements Self-inductance. Self-inductance. RL Circuit. RL Circuit, cont 3/11/2011. Chapter (not.9-.10) τ = R. Electromagnetic Waves
Chapter 21.8-13(not.9-.10) Electromagnetic Announcements Clicker quizzes NO LONGER GRADED! WebAssign HW Set 8 due this Friday Problems cover material from Chapters 21-22 Office hours: My office hours today
More informationMCQs E M WAVES. Physics Without Fear.
MCQs E M WAVES Physics Without Fear Electromagnetic Waves At A Glance Ampere s law B. dl = μ 0 I relates magnetic fields due to current sources. Maxwell argued that this law is incomplete as it does not
More informationTransformers. slide 1
Transformers an alternating emf V1 through the primary coil causes an oscillating magnetic flux through the secondary coil and, hence, an induced emf V2. The induced emf of the secondary coil is delivered
More informationPoynting Vector and Energy Flow W14D1
Poynting Vector and Energy Flow W14D1 1 Announcements Week 14 Prepset due online Friday 8:30 am PS 11 due Week 14 Friday at 9 pm in boxes outside 26-152 Sunday Tutoring 1-5 pm in 26-152 2 Outline Poynting
More informationPES 1120 Spring 2014, Spendier Lecture 38/Page 1
PES 1120 Spring 2014, Spendier Lecture 38/Page 1 Today: Start last chapter 32 - Maxwell s Equations James Clerk Maxwell (1831-1879) Scottish mathematical physicist. He united all observations, experiments
More informationDescribe 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 informationWorked Examples Set 2
Worked Examples Set 2 Q.1. Application of Maxwell s eqns. [Griffiths Problem 7.42] In a perfect conductor the conductivity σ is infinite, so from Ohm s law J = σe, E = 0. Any net charge must be on the
More informationLecture 33. PHYC 161 Fall 2016
Lecture 33 PHYC 161 Fall 2016 Faraday s law of induction When the magnetic flux through a single closed loop changes with time, there is an induced emf that can drive a current around the loop: Recall
More informationLecture 22 Chapter 31 Maxwell s equations
Lecture 22 Chapter 31 Maxwell s equations Finally, I see the goal, the summit of this Everest Today we are going to discuss: Chapter 31: Section 31.2-4 Let s revisit Ampere s Law a straight wire with current
More informationChapter 31. Faraday s Law
Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field dφ B ( I I ) E d s = µ o + d = µ o I+ µ oεo ds E B 2 Induction A loop of wire is connected to a sensitive
More informationCHAPTER 32: ELECTROMAGNETIC WAVES
CHAPTER 32: ELECTROMAGNETIC WAVES For those of you who are interested, below are the differential, or point, form of the four Maxwell s equations we studied this semester. The version of Maxwell s equations
More informationMaxwell s equations. Kyoto. James Clerk Maxwell. Physics 122. James Clerk Maxwell ( ) Unification of electrical and magnetic interactions
Maxwell s equations Physics /5/ Lecture XXIV Kyoto /5/ Lecture XXIV James Clerk Maxwell James Clerk Maxwell (83 879) Unification of electrical and magnetic interactions /5/ Lecture XXIV 3 Φ = da = Q ε
More informationElectromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance
Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic
More informationWhere k = 1. The electric field produced by a point charge is given by
Ch 21 review: 1. Electric charge: Electric charge is a property of a matter. There are two kinds of charges, positive and negative. Charges of the same sign repel each other. Charges of opposite sign attract.
More informationPhysics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3
Physics 201 p. 1/3 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/3 What are electromagnetic waves? Electromagnetic waves consist of electric fields and magnetic fields which
More informationELECTROMAGNETIC WAVES
UNIT V ELECTROMAGNETIC WAVES Weightage Marks : 03 Displacement current, electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic
More information1 Maxwell s Equations
PHYS 280 Lecture problems outline Spring 2015 Electricity and Magnetism We previously hinted a links between electricity and magnetism, finding that one can induce electric fields by changing the flux
More informationPHYS 1444 Section 003 Lecture #23
PHYS 1444 Section 3 Lecture #3 Monday, Nov. 8, 5 EM Waves from Maxwell s Equations Speed of EM Waves Light as EM Wave Electromagnetic Spectrum Energy in EM Waves Energy Transport The epilogue Today s homework
More informationMaxwell s equations and EM waves. From previous Lecture Time dependent fields and Faraday s Law
Maxwell s equations and EM waves This Lecture More on Motional EMF and Faraday s law Displacement currents Maxwell s equations EM Waves From previous Lecture Time dependent fields and Faraday s Law 1 Radar
More informationPoynting Theory & Wave Polarization
Poynting Theory & Wave Polarization Prepared By Dr. Eng. Sherif Hekal Assistant Professor Electronics and Communications Engineering 10/31/2017 1 Agenda Poynting Theory o Poynting Vector o Time average
More informationIntroduction 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 informationREVIEW SESSION. Midterm 2
REVIEW SESSION Midterm 2 Summary of Chapter 20 Magnets have north and south poles Like poles repel, unlike attract Unit of magnetic field: tesla Electric currents produce magnetic fields A magnetic field
More informationCHAPTER 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 informationElectromagnetic Waves
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 23 Electromagnetic Waves Marilyn Akins, PhD Broome Community College Electromagnetic Theory Theoretical understanding of electricity and magnetism
More informationDHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF EEE PART A. 1. Define mutual inductance and self inductance. (A/M-15)
DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF EEE EE6302-ELECTROMAGNETIC THEORY UNIT 4 PART A 1. Define mutual inductance and self inductance. (A/M-15) Self inductance is the ration between the induced
More informationINTRODUCTION ELECTRODYNAMICS BEFORE MAXWELL MAXWELL S DISPLACEMENT CURRENT. Introduction Z B S. E l = Electrodynamics before Maxwell
Chapter 14 MAXWELL S EQUATONS ntroduction Electrodynamics before Maxwell Maxwell s displacement current Maxwell s equations: General Maxwell s equations in vacuum The mathematics of waves Summary NTRODUCTON
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 Before Starting All of your grades should now be posted
More informationElectromagnetic Theory: PHAS3201, Winter Maxwell s Equations and EM Waves
Electromagnetic Theory: PHA3201, Winter 2008 5. Maxwell s Equations and EM Waves 1 Displacement Current We already have most of the pieces that we require for a full statement of Maxwell s Equations; however,
More informationIntroduction to Electromagnetism
Introduction to Electromagnetism Electric Field Lines If a charge feels an electrostatic force (Coulombic Force), it is said to be in an electric field. We like to represent electric fields with lines.
More informationOscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1
Oscillations and Electromagnetic Waves March 30, 2014 Chapter 31 1 Three Polarizers! Consider the case of unpolarized light with intensity I 0 incident on three polarizers! The first polarizer has a polarizing
More informationChapter 22. Induction
Chapter 22 Induction Induced emf A current can be produced by a changing magnetic field First shown in an experiment by Michael Faraday A primary coil is connected to a battery A secondary coil is connected
More informationElectromagnetic Waves Retarded potentials 2. Energy and the Poynting vector 3. Wave equations for E and B 4. Plane EM waves in free space
Electromagnetic Waves 1 1. Retarded potentials 2. Energy and the Poynting vector 3. Wave equations for E and B 4. Plane EM waves in free space 1 Retarded Potentials For volume charge & current = 1 4πε
More informationPart 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is
1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field
More informationChapter 33: ELECTROMAGNETIC WAVES 559
Chapter 33: ELECTROMAGNETIC WAVES 1 Select the correct statement: A ultraviolet light has a longer wavelength than infrared B blue light has a higher frequency than x rays C radio waves have higher frequency
More informationELECTROMAGNETIC WAVE PROPAGATION EC 442. Prof. Darwish Abdel Aziz
ELECTROMAGNETIC WAVE PROPAGATION EC 442 Prof. Darwish Abdel Aziz CHAPTER 6 LINEAR WIRE ANTENNAS INFINITESIMAL DIPOLE INTRODUCTION Wire antennas, linear or curved, are some of the oldest, simplest, cheapest,
More informationElectromagnetic Radiation
Electromagnetic Radiation Producing EMR All EMR is produced by accelerating charges Consists of changing electric and magnetic fields Speed of all EMR in vacuum is 3.00 x 10 8 m/s EMR is made up electric
More informationwe 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 information2426 Required Topics (May 4, 2012 draft) Halliday, FUNDAMENTALS OF PHYSICS, 9e Required topics are in bold text. Optional topics are in normal text.
2426 Required Topics (May 4, 2012 draft) Halliday, FUNDAMENTALS OF PHYSICS, 9e Required topics are in bold text. Optional topics are in normal text. Chapter 21 Electric Charge 21-1 What Is Physics? 21-2
More informationChapter 34. Electromagnetic Waves
Chapter 34 Electromagnetic Waves Waves If we wish to talk about electromagnetism or light we must first understand wave motion. If you drop a rock into the water small ripples are seen on the surface of
More informationwhere the last equality follows from the divergence theorem. Now since we did this for an arbitrary volume τ, it must hold locally:
8 Electrodynamics Read: Boas Ch. 6, particularly sec. 10 and 11. 8.1 Maxwell equations Some of you may have seen Maxwell s equations on t-shirts or encountered them briefly in electromagnetism courses.
More informationUNIT-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 informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 efore Starting All of your grades should now be posted
More informationCHAPTER 8 CONSERVATION LAWS
CHAPTER 8 CONSERVATION LAWS Outlines 1. Charge and Energy 2. The Poynting s Theorem 3. Momentum 4. Angular Momentum 2 Conservation of charge and energy The net amount of charges in a volume V is given
More informationUNIT 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 informationE.M.WAVES 1. Taller the antenna longer is the coverage of television broadcast. Justify this statement with the help of a figure. 2.If v g, v x v m represents the speed of gamma rays, X-rays microwaves
More informationEMF Notes 11; Maxwell s Equations. MAXWELL S EQUATIONS Maxwell s four equations
MAXWELL S EQUATONS Maxwell s four equations n the 870 s, James Clerk Maxwell showed that four equations constitute a complete description of the electric and magnetic fields, or THE ELECTROMAGNETC FELD
More informationElectromagnetic Waves
Chapter 32 Electromagnetic Waves PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 32 To learn why a light
More informationLast Homework. Reading: Chap. 33 and Chap. 33. Suggested exercises: 33.1, 33.3, 33.5, 33.7, 33.9, 33.11, 33.13, 33.15,
Chapter 33. Electromagnetic Induction Electromagnetic induction is the scientific principle that underlies many modern technologies, from the generation of electricity to communications and data storage.
More informationCourse Updates. 2) This week: Electromagnetic Waves +
Course Updates http://www.phys.hawaii.edu/~varner/phys272-spr1/physics272.html Reminders: 1) Assignment #11 due Wednesday 2) This week: Electromagnetic Waves + 3) In the home stretch [review schedule]
More informationr 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 informationPHYS 532 Lecture 10 Page Derivation of the Equations of Macroscopic Electromagnetism. Parameter Microscopic Macroscopic
PHYS 532 Lecture 10 Page 1 6.6 Derivation of the Equations of Macroscopic Electromagnetism Parameter Microscopic Macroscopic Electric Field e E = Magnetic Field b B = Charge Density η ρ = Current
More informationElectromagnetic 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 informationYell if you have any questions
Class 31: Outline Hour 1: Concept Review / Overview PRS Questions possible exam questions Hour : Sample Exam Yell if you have any questions P31 1 Exam 3 Topics Faraday s Law Self Inductance Energy Stored
More informationElectromagnetic (EM) Waves
Electromagnetic (EM) Waves Short review on calculus vector Outline A. Various formulations of the Maxwell equation: 1. In a vacuum 2. In a vacuum without source charge 3. In a medium 4. In a dielectric
More informationAC Circuits and Electromagnetic Waves
AC Circuits and Electromagnetic Waves Physics 102 Lecture 5 7 March 2002 MIDTERM Wednesday, March 13, 7:30-9:00 pm, this room Material: through next week AC circuits Next week: no lecture, no labs, no
More informationClass 15 : Electromagnetic Waves
Class 15 : Electromagnetic Waves Wave equations Why do electromagnetic waves arise? What are their properties? How do they transport energy from place to place? Recap (1) In a region of space containing
More informationDHANALAKSHMI 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 informationMotional Electromotive Force
Motional Electromotive Force The charges inside the moving conductive rod feel the Lorentz force The charges drift toward the point a of the rod The accumulating excess charges at point a create an electric
More informationElectromagnetic 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 informationChapter 8. Conservation Laws. 8.3 Magnetic Forces Do No Work
Chapter 8. Conservation Laws 8.3 Magnetic Forces Do No Work 8.2 Momentum of EM fields 8.2.1 Newton's Third Law in Electrodynamics Consider two charges, q 1 and q 2, moving with speeds v 1 and v 2 magnetic
More informationTECHNO 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 informationCHAPTER 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 informationPHYS 1441 Section 001 Lecture #24 Wednesday, Dec. 6, 2017 Dr. Animesh Chatterjee
PHYS 1441 Section 1 Lecture #4 Dr. Animesh Chatterjee Chapter 3: Inductance AC Circuit W/ LRC Chapter 31: Maxwell s Equations Expansion of Ampere s Law Gauss Law for Magnetism Production of EM Waves Light
More informationElectromagnetic Induction and Waves (Chapters 33-34)
Electromagnetic nduction and Waves (Chapters 33-34) The laws of emf induction: Faraday s and Lenz s laws Concepts of classical electromagnetism. Maxwell equations nductance Mutual inductance M Self inductance
More informationInductors Maxwell s equations
Lecture 19 Chapter 34 Physics II Inductors Maxwell s equations Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Inductors Inductors (solenoids) store potential energy in a form
More informationChapter 31: Electromagnetic Induction and Faraday s Law All sections covered.
About Exam 3 When and where (same as before) Monday Nov. 22 rd 5:30-7:00 pm Bascom 272: Sections 301, 302, 303, 304, 305, 311,322, 327, 329 Ingraham B10: Sections 306, 307, 312, 321, 323, 324, 325, 328,
More informationElectromagnetic Theory Prof. D. K. Ghosh Department of Physics Indian Institute of Technology, Bombay
Electromagnetic Theory Prof. D. K. Ghosh Department of Physics Indian Institute of Technology, Bombay Module - 4 Time Varying Field Lecture - 30 Maxwell s Equations In the last lecture we had introduced
More informationEnergy Carried by Electromagnetic Waves. Momentum and Radiation Pressure of an Electromagnetic Wave.
Today s agenda: Electromagnetic Waves. Energy Carried by Electromagnetic Waves. Momentum and Radiation Pressure of an Electromagnetic Wave. Maxwell s Equations Recall: EdA Eds q enclosed o d dt B Bds=μ
More informationChapter 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 informationLecture 13.2 :! Inductors
Lecture 13.2 :! Inductors Lecture Outline:! Induced Fields! Inductors! LC Circuits! LR Circuits!! Textbook Reading:! Ch. 33.6-33.10 April 9, 2015 1 Announcements! HW #10 due on Tuesday, April 14, at 9am.!
More informationqq k d Chapter 16 Electric and Magnetic Forces Electric charge Electric charges Negative (electron) Positive (proton)
Chapter 16 Electric and Magnetic Forces Electric charge Electric charges Negative (electron) Positive (proton) Electrons and protons in atoms/molecules Ions: atoms/molecules with excess of charge Ions
More informationIntermission Page 343, Griffith
Intermission Page 343, Griffith Chapter 8. Conservation Laws (Page 346, Griffith) Lecture : Electromagnetic Power Flow Flow of Electromagnetic Power Electromagnetic waves transport throughout space the
More informationAP 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 informationPrinciples of Mobile Communications
Communication Networks 1 Principles of Mobile Communications University Duisburg-Essen WS 2003/2004 Page 1 N e v e r s t o p t h i n k i n g. Wave Propagation Single- and Multipath Propagation Overview:
More informationElectromagnetic Waves
Physics 102: Lecture 15 Electromagnetic Waves Energy & Polarization Physics 102: Lecture 15, Slide 1 Checkpoint 1.1, 1.2 y E x loop in xy plane loop in xz plane A B C Physics 102: Lecture 15, Slide 2 Propagation
More information4. The last equation is Ampère's Law, which ultimately came from our derivation of the magnetic field from Coulomb's Law and special relativity.
lectromagnetic Theory Prof Ruiz, UNC Asheville, doctorphys on YouTube Chapter G Notes Maxwell's quations: Integral Form G1 No Magnetic Monopoles Q da ε da dl dl µ I The equations at the left summarize
More informationPhysics 2102 Gabriela González. Marathon review of the course: 15 weeks in ~60 minutes!
Physics 2102 Gabriela González Marathon review of the course: 15 weeks in ~60 minutes! Fields: electric & magnetic electric and magnetic forces on electric charges potential energy, electric potential,
More information