Indiana University Physics P331: Theory of Electromagnetism Review Problems #3
|
|
- Samantha Hudson
- 5 years ago
- Views:
Transcription
1 Indiana University Physics P331: Theory of Electromagnetism Review Problems #3 Note: The final exam (Friday 1/14 8:00-10:00 AM will be comprehensive, covering lecture and homework material pertaining to HW #1-1. The following review problems cover material not included in Exams 1 and. 1. The boundary between two linear dielectric materials with different permittivities is given by the z = 0 plane with ɛ 1 above and ɛ below the plane. Identify the correct formula(s satisfied by the normal derivative of V at the boundary (that is, the derivative of V in the direction normal to the boundary. Recall E = V, and V 1 refers to the potential in region 1 and V refers to the potential in region. (a V 1 V = σ free (b V 1 z (c ɛ 1 V 1 z (d ɛ 1 V 1 z z=0 V = σtot ɛ 0 V z=0 ɛ z = σ free V z=0 ɛ = σ bound ɛ 0. Which of the following is a statement of charge conservation? (a ρ t = J (b ρ t = S J d a (c ρ t = V J dτ (d None of the above. 3. Why can t we use a scalar potential to find the (static magnetic field, as we have done with the (static electric field, i.e., why can t we use B( r = V B ( r (a Because the divergence of B is always zero (no magnetic monopoles. (b Because only either E or B can be described with a scalar potential, not both. (c Because B can have a non-zero curl according to Ampere s law: B = µ 0 J. (d None of the above. 1
2 4. A laterally large plane of charge with surface charge density σ f sits between two (large neutral, linear dielectric wafers (dielectric constant ɛ r, as shown. +"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"+"! f (a Determine D and E everywhere in space. (b Find the polarization density P inside the wafers. (c Determine any discontinuities in D and E at all boundaries. 5. A coaxial cable consists of a copper wire of radius R 1, surrounded by a concentric copper tube of inner radius R and outer radius R 3. The space between is filled with material of dielectric constant ɛ r. Find the capacitance per unit length of the cable. 6. A spherical conductor of radius R 1, is uniformly charged, with surface charge density σ 0. It is coated with a neutral, linear dielectric of susceptibility χ e from r = R 1 to r = R. (a What is the electric field, E, outside the coating, for r > R? (b What is the electric field, E, within the bulk of the coating, for R 1 < r < R? (c What are the bound surface charge densities at r = R 1 and r = R? What is the bound volume charge density in the region R 1 < r < R? (d What boundary conditions does E satisfy at r = R 1 and r = R? Show that the solutions in parts (a and (b are consistent with these boundary conditions. (e Find the bound surface and volume charge densities, σ b and ρ b, respectively. 7. A segment of wire is bent into an arc of radius R and subtended angle θ. Point P is at the center of the circular segment. The wire carries constant current, I. (a What is the magnetic field at P? (b An electron is located at P, moving at v = v 0ˆx. What is the magnetic force on the electron?
3 8. A thick slab of nonmagnetic material carries a uniform volume current density, J = J ˆx as shown in the figure. The slab is infinite in the x and y directions and extends from z = a to z = +a. (a Find the magnetic field inside the slab. (b Find the magnetic field outside the slab. 9. Consider a long wire of radius a, and suppose that the current density within the wire has the form: J(s = I 0 s π a 4, in units of Amps per square meter, where s is the radial distance from the axis of the wire, and the direction of J is along the wire. (a What is the total current I running through the wire? (b What is the magnitude of the magnetic field at points outside the wire (i.e., for s > a? (c What is the magnitude of the magnetic field at points inside the wire (i.e., for s < a? 10. The polarizability, α, of a methane molecule is given cm 3 : recall p = α E. The atomic polarizability of a carbon atom is cm 3, and that of hyrdogen is cm 3. Comment on the effect of binding of atoms into a molecule on the electronic structure. Recall that methane is CH Consider two water molecules, each with dipole moment p = Cm. Determine the dipole-dipole interaction force between them (responsible for hydrogen bonding when they are a distance r = 1 nm apart for the special cases where (a ˆp 1 = ˆp and ˆp 1 ˆr = ˆp ˆr = 0. (b ˆp 1 = ˆp = ˆr Recall that the potential energy of a dipole in an electric field is given by U = p E and the electric field of a dipole oriented in the z direction is E = 1 p ( cos θ ˆr + sin θ 4πɛ 0 r ˆθ 3 3
4 1. A long, thick cylindrical shell of inner radius a and outer radius b is made of dielectric material with frozen-in polarization given by P = k s ŝ (a Locate all the bound surface and volume charge densities. (b Use Gauss law to find the electric field in all three regions 0 < s a, a s b and s b. 4
5 Formula Sheet E(r = 1 ρ(r r r ( r r r r dτ, (Coulomb s Law V = U/q, (Electric Potential Difference ˆ r V (r = E dl, E = V, (Def n of Electric Potential O ˆˆ O E da = 1 ε 0 q enclosed, E = 1 ε 0 ρ, (Gauss s Law E dl = 0, E = 0, (Path Indep. of Elec. Potential V (r = 1 ˆˆ O F da = ρ(r r r dτ, (Coulomb s Law for Potential [V = 0] ( F dτ (Divergence Theorem ˆˆ F dl = ( F da, (Stokes Theorem ˆ b ( ψ dl = ψ(b ψ(a, a (Fundamental Theorem for Gradients U = 1 ρ(rv (r dτ = ε 0 E(r dτ, (Electrostatic Potential Energy C = Q/ V, (Capacitance 5
6 More possibly useful formulas, etc Poisson s Equation [Laplace s Equation] V = 1 ε 0 ρ [ V = 0] General solution to Laplace s Equation in spherical polar coordinates Boundary Conditions (so far V (r, θ = l=0 ( A l r l 1 + B l P r l+1 n (cos θ, E E 1 = σ/ɛ 0, E 1 = E V 1 = V. V ( r = 1 n=0 1 r n+1 ρ( r (r n P n (cos θ dτ, (Multipole expansion V ( r = 1 p ˆr r, (Dipole potential E( r = 1 p ( cos θˆr + sin θˆθ, (Dipole in electric field 4πɛ 0 r 3 p = i q ir i, p = ρ( r r dτ, (Dipole moment P 0 (x = 1, P 1 (x = x, P (x = (3x 1/, P 3 (x = (5x 3 3x/, (Legendre Polynomials cosh u = eu + e u, sinh u = eu e u, (Hyperbolic Sine/Cosine D ε 0 E+P, (Def n. of Electric Displacement Vector D = ρ free, σ b = P ˆn, ρ b = P, (Gauss s Law in mat l, bound charge densities 6
7 P = χ e ε 0 E, ε ε 0 (1 + χ e, (Linear Dielectrics J = ρ t, (Continuity Equation ˆ I = J da (Current and Current Density B(r = µ 0 4π C ˆ I(r dl (r r r r 3, (Biot-Savart Law B dl = µ 0 I enclosed, B = µ 0 J (Integral/Differential Forms of Ampere s Law E = 1 ρ, ɛ 0 E = 0, B = 0, B = µ 0 J (Maxwell s equations for static charge and current distributions in vacuum P 0 (x = 1, P 1 (x = x, P (x = (3x 1/, P 3 (x = (5x 3 3x/, (Legendre Polynomials 7
Electromagnetism: Worked Examples. University of Oxford Second Year, Part A2
Electromagnetism: Worked Examples University of Oxford Second Year, Part A2 Caroline Terquem Department of Physics caroline.terquem@physics.ox.ac.uk Michaelmas Term 2017 2 Contents 1 Potentials 5 1.1 Potential
More informationChapter 4. Electrostatic Fields in Matter
Chapter 4. Electrostatic Fields in Matter 4.1. Polarization 4.2. The Field of a Polarized Object 4.3. The Electric Displacement 4.4. Linear Dielectrics 4.5. Energy in dielectric systems 4.6. Forces on
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 informationl=0 The expansion coefficients can be determined, for example, by finding the potential on the z-axis and expanding that result in z.
Electrodynamics I Exam - Part A - Closed Book KSU 15/11/6 Name Electrodynamic Score = 14 / 14 points Instructions: Use SI units. Where appropriate, define all variables or symbols you use, in words. Try
More informationlim = F F = F x x + F y y + F z
Physics 361 Summary of Results from Lecture Physics 361 Derivatives of Scalar and Vector Fields The gradient of a scalar field f( r) is given by g = f. coordinates f g = ê x x + ê f y y + ê f z z Expressed
More informationCHAPTER 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 informationCurrents (1) Line charge λ (C/m) with velocity v : in time t, This constitutes a current I = λv (vector). Magnetic force on a segment of length dl is
Magnetostatics 1. Currents 2. Relativistic origin of magnetic field 3. Biot-Savart law 4. Magnetic force between currents 5. Applications of Biot-Savart law 6. Ampere s law in differential form 7. Magnetic
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 informationLecture notes for ELECTRODYNAMICS.
Lecture notes for 640-343 ELECTRODYNAMICS. 1 Summary of Electrostatics 1.1 Coulomb s Law Force between two point charges F 12 = 1 4πɛ 0 Q 1 Q 2ˆr 12 r 1 r 2 2 (1.1.1) 1.2 Electric Field For a charge distribution:
More informationSummary: Applications of Gauss Law
Physics 2460 Electricity and Magnetism I, Fall 2006, Lecture 15 1 Summary: Applications of Gauss Law 1. Field outside of a uniformly charged sphere of radius a: 2. An infinite, uniformly charged plane
More informationPhysics 505 Fall 2005 Homework Assignment #7 Solutions
Physics 505 Fall 005 Homework Assignment #7 Solutions Textbook problems: Ch. 4: 4.10 Ch. 5: 5.3, 5.6, 5.7 4.10 Two concentric conducting spheres of inner and outer radii a and b, respectively, carry charges
More informationElectric fields in matter
Electric fields in matter November 2, 25 Suppose we apply a constant electric field to a block of material. Then the charges that make up the matter are no longer in equilibrium: the electrons tend to
More informationChapter 21: Gauss law Tuesday September 13 th. Gauss law and conductors Electrostatic potential energy (more likely on Thu.)
Chapter 21: Gauss law Tuesday September 13 th LABS START THIS WEEK Quick review of Gauss law The flux of a vector field The shell theorem Gauss law for other symmetries A uniformly charged sheet A uniformly
More informationJunior-level Electrostatics Content Review
Junior-level Electrostatics Content Review Please fill out the following exam to the best of your ability. This will not count towards your final grade in the course. Do your best to get to all the questions
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 informationIMPORTANT: LABS START NEXT WEEK
Chapter 21: Gauss law Thursday September 8 th IMPORTANT: LABS START NEXT WEEK Gauss law The flux of a vector field Electric flux and field lines Gauss law for a point charge The shell theorem Examples
More informationTutorial 3 - Solutions Electromagnetic Waves
Tutorial 3 - Solutions Electromagnetic Waves You can find formulas you require for vector calculus at the end of this tutorial. 1. Find the Divergence and Curl of the following functions - (a) k r ˆr f
More informationProblem Set #4: 4.1,4.7,4.9 (Due Monday, March 25th)
Chapter 4 Multipoles, Dielectrics Problem Set #4: 4.,4.7,4.9 (Due Monday, March 5th 4. Multipole expansion Consider a localized distribution of charges described by ρ(x contained entirely in a sphere of
More informationChapter 30 Sources of the magnetic field
Chapter 30 Sources of the magnetic field Force Equation Point Object Force Point Object Field Differential Field Is db radial? Does db have 1/r2 dependence? Biot-Savart Law Set-Up The magnetic field is
More informationPhysics 202, Lecture 13. Today s Topics. Magnetic Forces: Hall Effect (Ch. 27.8)
Physics 202, Lecture 13 Today s Topics Magnetic Forces: Hall Effect (Ch. 27.8) Sources of the Magnetic Field (Ch. 28) B field of infinite wire Force between parallel wires Biot-Savart Law Examples: ring,
More informationChapter 5. Magnetostatics
Chapter 5. Magnetostatics 5.4 Magnetic Vector Potential 5.1.1 The Vector Potential In electrostatics, E Scalar potential (V) In magnetostatics, B E B V A Vector potential (A) (Note) The name is potential,
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 informationThere are four questions on this exam. All are of equal value but not necessarily of equal difficulty. Answer all four questions
Electricity and Magnetism (PHYS2016) Second Semester Final Exam 2015 There are four questions on this exam. All are of equal value but not necessarily of equal difficulty. Answer all four questions You
More information1. (3) Write Gauss Law in differential form. Explain the physical meaning.
Electrodynamics I Midterm Exam - Part A - Closed Book KSU 204/0/23 Name Instructions: Use SI units. Where appropriate, define all variables or symbols you use, in words. Try to tell about the physics involved,
More informationThe Steady Magnetic Field LECTURE 7
The Steady Magnetic Field LECTURE 7 Learning Objectives Understand the Biot-Savart Law Understand the Ampere s Circuital Law Explain the Application of Ampere s Law Motivating the Magnetic Field Concept:
More informationSolution Set Eight. 1 Problem #1: Toroidal Electromagnet with Gap Problem #4: Self-Inductance of a Long Solenoid. 9
: Solution Set Eight Northwestern University, Electrodynamics I Wednesday, March 9, 6 Contents Problem #: Toroidal Electromagnet with Gap. Problem #: Electromagnetic Momentum. 3 3 Problem #3: Type I Superconductor.
More informationweek 3 chapter 28 - Gauss s Law
week 3 chapter 28 - Gauss s Law Here is the central idea: recall field lines... + + q 2q q (a) (b) (c) q + + q q + +q q/2 + q (d) (e) (f) The number of electric field lines emerging from minus the number
More informationElectrostatics. Chapter Maxwell s Equations
Chapter 1 Electrostatics 1.1 Maxwell s Equations Electromagnetic behavior can be described using a set of four fundamental relations known as Maxwell s Equations. Note that these equations are observed,
More informationfree space (vacuum) permittivity [ F/m]
Electrostatic Fields Electrostatic fields are static (time-invariant) electric fields produced by static (stationary) charge distributions. The mathematical definition of the electrostatic field is derived
More informationLecture 13: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay. Poisson s and Laplace s Equations
Poisson s and Laplace s Equations Lecture 13: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We will spend some time in looking at the mathematical foundations of electrostatics.
More informationAMPERE'S LAW. B dl = 0
AMPERE'S LAW The figure below shows a basic result of an experiment done by Hans Christian Oersted in 1820. It shows the magnetic field produced by a current in a long, straight length of current-carrying
More informationPhysics 202, Lecture 3. The Electric Field
Physics 202, Lecture 3 Today s Topics Electric Field (Review) Motion of charged particles in external E field Conductors in Electrostatic Equilibrium (Ch. 21.9) Gauss s Law (Ch. 22) Reminder: HW #1 due
More informationDIVERGENCE AND CURL THEOREMS
This document is stored in Documents/4C/Gausstokes.tex. with LaTex. Compile it November 29, 2014 Hans P. Paar DIVERGENCE AND CURL THEOREM 1 Introduction We discuss the theorems of Gauss and tokes also
More informationINTRODUCTION 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 information1. (3) Write Gauss Law in differential form. Explain the physical meaning.
Electrodynamics I Midterm Exam - Part A - Closed Book KSU 204/0/23 Name Electro Dynamic Instructions: Use SI units. Where appropriate, define all variables or symbols you use, in words. Try to tell about
More informationfiziks 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 informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Spring 2013 Exam 3 Equation Sheet. closed fixed path. ! = I ind.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.0 Spring 013 Exam 3 Equation Sheet Force Law: F q = q( E ext + v q B ext ) Force on Current Carrying Wire: F = Id s " B # wire ext Magnetic
More informationChapter 5. Magnetostatics
Chapter 5. Magnetostatics 5.1 The Lorentz Force Law 5.1.1 Magnetic Fields Consider the forces between charges in motion Attraction of parallel currents and Repulsion of antiparallel ones: How do you explain
More informationFORMULA SHEET FOR QUIZ 2 Exam Date: November 8, 2017
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.07: Electromagnetism II November 5, 207 Prof. Alan Guth FORMULA SHEET FOR QUIZ 2 Exam Date: November 8, 207 A few items below are marked
More informationE&M. 1 Capacitors. January 2009
E&M January 2009 1 Capacitors Consider a spherical capacitor which has the space between its plates filled with a dielectric of permittivity ɛ. The inner sphere has radius r 1 and the outer sphere has
More informationChapter 4. Electric Fields in Matter
Chapter 4. Electric Fields in Matter 4.1.2 Induced Dipoles What happens to a neutral atom when it is placed in an electric field E? The atom now has a tiny dipole moment p, in the same direction as E.
More informationNIU Ph.D. Candidacy Examination Fall 2018 (8/21/2018) Electricity and Magnetism
NIU Ph.D. Candidacy Examination Fall 2018 (8/21/2018) Electricity and Magnetism You may solve ALL FOUR problems if you choose. The points of the best three problems will be counted towards your final score
More informationINSTITUTE 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 informationProblem Set #3: 2.11, 2.15, 2.21, 2.26, 2.40, 2.42, 2.43, 2.46 (Due Thursday Feb. 27th)
Chapter Electrostatics Problem Set #3:.,.5,.,.6,.40,.4,.43,.46 (Due Thursday Feb. 7th). Coulomb s Law Coulomb showed experimentally that for two point charges the force is - proportional to each of the
More informationRelevant Electrostatics and Magnetostatics (Old and New)
Unit 1 Relevant Electrostatics and Magnetostatics (Old and New) The whole of classical electrodynamics is encompassed by a set of coupled partial differential equations (at least in one form) bearing the
More informationElectrodynamics I Midterm - Part A - Closed Book KSU 2005/10/17 Electro Dynamic
Electrodynamics I Midterm - Part A - Closed Book KSU 5//7 Name Electro Dynamic. () Write Gauss Law in differential form. E( r) =ρ( r)/ɛ, or D = ρ, E= electricfield,ρ=volume charge density, ɛ =permittivity
More informationHomework Assignment 4 Solution Set
Homework Assignment 4 Solution Set PHYCS 442 7 February, 24 Problem (Griffiths 2.37 If the plates are sufficiently large the field near them does not depend on d. The field between the plates is zero (the
More informationElectricity & 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 informationINSTITUTE 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 informationThe Steady Magnetic Fields
The Steady Magnetic Fields Prepared By Dr. Eng. Sherif Hekal Assistant Professor Electronics and Communications Engineering 1/8/017 1 Agenda Intended Learning Outcomes Why Study Magnetic Field Biot-Savart
More informationECE 3209 Electromagnetic Fields Final Exam Example. University of Virginia Solutions
ECE 3209 Electromagnetic Fields Final Exam Example University of Virginia Solutions (print name above) This exam is closed book and closed notes. Please perform all work on the exam sheets in a neat and
More informationFlux. Flux = = va. This is the same as asking What is the flux of water through the rectangle? The answer depends on:
Ch. 22: Gauss s Law Gauss s law is an alternative description of Coulomb s law that allows for an easier method of determining the electric field for situations where the charge distribution contains symmetry.
More informationUNIVERSITY OF CALIFORNIA - SANTA CRUZ DEPARTMENT OF PHYSICS PHYS 110A. Homework #6. Benjamin Stahl. February 17, 2015
UNIVERSITY OF CALIFORNIA - SANTA CRUZ DEPARTMENT OF PHYSICS PHYS A Homework #6 Benjamin Stahl February 7, 5 GRIFFITHS, 5.9 The magnetic field at a point, P, will be found for each of the steady current
More informationMagnetostatics and the vector potential
Magnetostatics and the vector potential December 8, 2015 1 The divergence of the magnetic field Starting with the general form of the Biot-Savart law, B (x 0 ) we take the divergence of both sides with
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Spring 2014 Final Exam Equation Sheet. B( r) = µ o 4π
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2014 Final Exam Equation Sheet Force Law: F q = q( E ext + v q B ext ) Poynting Vector: S = ( E B) / µ 0 Force on Current Carrying
More informationElectrodynamics Exam 3 and Final Exam Sample Exam Problems Dr. Colton, Fall 2016
Electrodynamics Exam 3 and Final Exam Sample Exam Problems Dr. Colton, Fall 016 Multiple choice conceptual questions 1. An infinitely long, straight wire carrying current passes through the center of a
More informationAP Physics C. Magnetism - Term 4
AP Physics C Magnetism - Term 4 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the world
More informationPart 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 informationA cylinder in a magnetic field (Jackson)
Problem 1. A cylinder in a magnetic field (Jackson) A very long hollow cylinder of inner radius a and outer radius b of permeability µ is placed in an initially uniform magnetic field B o at right angles
More informationCHETTINAD COLLEGE OF ENGINEERING & TECHNOLOGY NH-67, TRICHY MAIN ROAD, PULIYUR, C.F , KARUR DT.
CHETTINAD COLLEGE OF ENGINEERING & TECHNOLOGY NH-67, TRICHY MAIN ROAD, PULIYUR, C.F. 639 114, KARUR DT. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING COURSE MATERIAL Subject Name: Electromagnetic
More informationAP Physics C. Electricity - Term 3
AP Physics C Electricity - Term 3 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the
More informationPreliminary Exam: Electromagnetism, Thursday January 12, :00-12:00
1 Preliminary Exam: Electromagnetism, Thursday January 12, 2017. 9:00-12:00 Answer a total of any THREE out of the four questions. For your answers you can use either the blue books or individual sheets
More informationLecture 4-1 Physics 219 Question 1 Aug Where (if any) is the net electric field due to the following two charges equal to zero?
Lecture 4-1 Physics 219 Question 1 Aug.31.2016. Where (if any) is the net electric field due to the following two charges equal to zero? y Q Q a x a) at (-a,0) b) at (2a,0) c) at (a/2,0) d) at (0,a) and
More informationReview of Electrostatics
Review of Electrostatics 1 Gradient Define the gradient operation on a field F = F(x, y, z) by; F = ˆx F x + ŷ F y + ẑ F z This operation forms a vector as may be shown by its transformation properties
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 informationPhysics 3323, Fall 2016 Problem Set 2 due Sep 9, 2016
Physics 3323, Fall 26 Problem Set 2 due Sep 9, 26. What s my charge? A spherical region of radius R is filled with a charge distribution that gives rise to an electric field inside of the form E E /R 2
More informationChapter 27 Sources of Magnetic Field
Chapter 27 Sources of Magnetic Field In this chapter we investigate the sources of magnetic of magnetic field, in particular, the magnetic field produced by moving charges (i.e., currents). Ampere s Law
More informationMarch 11. Physics 272. Spring Prof. Philip von Doetinchem
Physics 272 March 11 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 32 Summary Magnetic
More informationUniversity of Illinois at Chicago Department of Physics
University of Illinois at Chicago Department of Physics Electromagnetism Qualifying Examination January 4, 2017 9.00 am - 12.00 pm Full credit can be achieved from completely correct answers to 4 questions.
More informationThe Steady Magnetic Field
The Steady Magnetic Field Prepared By Dr. Eng. Sherif Hekal Assistant Professor Electronics and Communications Engineering 1/13/016 1 Agenda Intended Learning Outcomes Why Study Magnetic Field Biot-Savart
More informationReview of Electrodynamics
Review of Electrodynamics VBS/MRC Review of Electrodynamics 0 First, the Questions What is light? How does a butterfly get its colours? How do we see them? VBS/MRC Review of Electrodynamics 1 Plan of Review
More informationLecture 20 Ampère s Law
Lecture 20 Ampère s Law Sections: 7.2, partially 7.7 Homework: See homework file Ampère s Law in ntegral Form 1 the field of a straight wire with current (Lecture 19) B H = = a a φ φ µ, T 2πρ, A/m 2πρ
More informationPhysics 208, Spring 2016 Exam #3
Physics 208, Spring 206 Exam #3 A Name (Last, First): ID #: Section #: You have 75 minutes to complete the exam. Formulae are provided on an attached sheet. You may NOT use any other formula sheet. You
More informationPhysics 202, Lecture 14
Physics 202, Lecture 14 Today s Topics Sources of the Magnetic Field (Ch. 30) Review: iot-savart Law, Ampere s Law Displacement Current: Ampere-Maxwell Law Magnetism in Matter Maxwell s Equations (prelude)
More informationReview of Electrostatics. Define the gradient operation on a field F = F(x, y, z) by;
Review of Electrostatics 1 Gradient Define the gradient operation on a field F = F(x, y, z) by; F = ˆx F x + ŷ F y + ẑ F z This operation forms a vector as may be shown by its transformation properties
More informationELECTRICITY 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 informationCLASSICAL ELECTRODYNAMICS I Physics 6/75203 SPRING 2013
INSTRUCTOR: CLASSICAL ELECTRODYNAMICS I Physics 6/75203 SPRING 2013 Dr. Mark Manley manley@kent.edu 220 Smith Hall http://www.kent.edu/cas/physics/people/manley.cfm 330-672-2407 CLASS HOURS: 1:10-2:00
More informationPHYS4210 Electromagnetic Theory Spring Final Exam Wednesday, 6 May 2009
Name: PHYS4210 Electromagnetic Theory Spring 2009 Final Exam Wednesday, 6 May 2009 This exam has two parts. Part I has 20 multiple choice questions, worth two points each. Part II consists of six relatively
More informationProblem Set #5: 5.7,5.9,5.13 (Due Monday, April 8th)
Chapter 5 Magnetostatics Problem Set #5: 5.7,5.9,5.13 (Due Monday, April 8th) 5.1 Biot-Savart Law So far we were concerned with static configuration of charges known as electrostatics. We now switch to
More informationMagnetostatics. Lecture 23: Electromagnetic Theory. Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Magnetostatics Lecture 23: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Magnetostatics Up until now, we have been discussing electrostatics, which deals with physics
More informationElectric Flux. If we know the electric field on a Gaussian surface, we can find the net charge enclosed by the surface.
Chapter 23 Gauss' Law Instead of considering the electric fields of charge elements in a given charge distribution, Gauss' law considers a hypothetical closed surface enclosing the charge distribution.
More informationLecture 15 Perfect Conductors, Boundary Conditions, Method of Images
Lecture 15 Perfect Conductors, Boundary Conditions, Method of Images Sections: 5.4, 5.5 Homework: See homework file Perfect Conductors 1 metals such as Cu, Ag, Al are closely approximated by the concept
More informationST.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 informationMaxwell s equations for electrostatics
Maxwell s equations for electrostatics October 6, 5 The differential form of Gauss s law Starting from the integral form of Gauss s law, we treat the charge as a continuous distribution, ρ x. Then, letting
More informationDielectrics. Lecture 20: Electromagnetic Theory. Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
What are dielectrics? Dielectrics Lecture 20: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay So far we have been discussing electrostatics in either vacuum or in a conductor.
More informationPhysics 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 information1 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 informationPhysics 8.02 Exam Two Equation Sheet Spring 2004
Physics 8.0 Exam Two Equation Sheet Spring 004 closed surface EdA Q inside da points from inside o to outside I dsrˆ db 4o r rˆ points from source to observer V moving from a to b E ds 0 V b V a b E ds
More informationMansfield 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 informationRead this cover page completely before you start.
I affirm that I have worked this exam independently, without texts, outside help, integral tables, calculator, solutions, or software. (Please sign legibly.) Read this cover page completely before you
More informationDielectrics - III. Lecture 22: Electromagnetic Theory. Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Dielectrics - III Lecture 22: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We continue with our discussion of dielectric medium. Example : Dielectric Sphere in a uniform
More informationMagnetostatic Fields. Dr. Talal Skaik Islamic University of Gaza Palestine
Magnetostatic Fields Dr. Talal Skaik Islamic University of Gaza Palestine 01 Introduction In chapters 4 to 6, static electric fields characterized by E or D (D=εE) were discussed. This chapter considers
More informationColumbia University Department of Physics QUALIFYING EXAMINATION
Columbia University Department of Physics QUALIFYING EXAMINATION Monday, January 9, 217 3:PM to 5:PM Classical Physics Section 2. Electricity, Magnetism & Electrodynamics Two hours are permitted for the
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 informationField Theory exam II Solutions
Field Theory exam II Solutions Problem 1 (a) Consider point charges, one with charge q located at x 1 = (1, 0, 1), and the other one with charge q at x = (1, 0, 1). Compute the multipole moments q lm in
More informationElectromagnetic Field Theory (EMT)
Electromagnetic Field Theory (EMT) Lecture # 9 1) Coulomb s Law and Field Intensity 2) Electric Fields Due to Continuous Charge Distributions Line Charge Surface Charge Volume Charge Coulomb's Law Coulomb's
More informationContents. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU.
1 Contents 5 Magnetostatics 3 5.1 Magnetic forces and torques............... 4 5.1.1 Magnetic force on a current-carrying conductor 8 5.1.2 Magnetic torque on a current-carrying loop.. 16 5.2 Biot-Savart
More informationElectric Flux Density, Gauss s Law and Divergence
Unit 3 Electric Flux Density, Gauss s Law and Divergence 3.1 Electric Flux density In (approximately) 1837, Michael Faraday, being interested in static electric fields and the effects which various insulating
More informationA half submerged metal sphere (UIC comprehensive
Problem 1. exam) A half submerged metal sphere (UIC comprehensive A very light neutral hollow metal spherical shell of mass m and radius a is slightly submerged by a distance b a below the surface of a
More informationElectric Field. Electric field direction Same direction as the force on a positive charge Opposite direction to the force on an electron
Electric Field Electric field Space surrounding an electric charge (an energetic aura) Describes electric force Around a charged particle obeys inverse-square law Force per unit charge Electric Field Electric
More information