Physics 322 Midterm 2
|
|
- Jonah McCormick
- 5 years ago
- Views:
Transcription
1 Physics 3 Midterm Nov 30, 015 name: Box your final answer. 1 (15 pt) (50 pt) 3 (0 pt) 4 (15 pt) total (100 pt) 1
2 1. (15 pt) An infinitely long cylinder of radius R whose axis is parallel to the ẑ axis has a uniform magnetization M = Mẑ. Compute H everywhere. ans Method 1: (5 pt H = 0; 3 pt H = M; 5 pt z [MΘ(s R)] = 0; pt concluding H = 0) Since J f = 0, we know H = 0 and H = M = [MẑΘ(s R)] = [MΘ(s R)] = 0. z Hence H = 0 everywhere. Method : (5 pt K b = M ˆn = M ˆφ; 5 pt writing down Ampere s law; 3 pt computing B z = µ 0 M; pt computing H = 0) Since M = 0, we conclude J b = 0. Since K b = M ˆn, we conclude K b = Mẑ ŝ = M ˆφ. Using Ampere s law, we find B z l = µ 0 K b ˆφl B z = µ 0 M H = B µ 0 M = Mẑ + Mẑ = 0 inside. Outside, there is no B for an infinite solenoid: H = 0.
3 . Suppose for t < 0, the capacitor is charged to V 0 in the circuit below. The switch is closed at t = 0. a) (10 pt) The current behaves as a function of time as I(t) = (envelope function of time) cos( ft + δ) where f > 0 for (R/L) < 4/(LC). What is f? ans (5 pt IR V L di dt = 0; 3 pt iωr + 1 C Lω = 0; pt taking the real part of quadratic equation solution correctly) Following the current and the potential drops (where we denote V as the capacitor potential), we have IR V L di dt = 0 Putting in we find Hence, we conclude f = Rω = IR Q C LdI dt = 0 di dt R + I C + Ld I dt = 0 I = I 0 e iωt, iωr + 1 C Lω = 0 ω = ir ± 4L C R L 4L C R L = 1 LC R 4L b) (15 pt) Suppose the inductance L is due to the self-inductance of a toroidal coil with rectangular cross section (innder radius a, outer radius b, and height h as shown in the figure below) carrying a total of N turns. Express L in terms of N, h, a, and b. ans (4 pt Ampere s law; 5 pt Φ = LI; 5 pt Φ computation; 1 pt answer) 3
4 Use Ampere s law: we have d l B = µ 0 NI, B φ = µ 0NI πs Using Φ = LI, we conclude Φ = Nh ˆ b a dsb φ = µ 0N Ih ln b π a L = µ 0N h π ln b a c) (10 pt) Suppose the toroidal coil described in part b) has a magnetic field B(s,φ,z) = f (s) ˆφ (where s is a cylindrical coordinate variable: e.g. the inner radius is described as s = a). In this magnetic field, suppose a pointlike magnetic dipole with m = mẑ is placed at rest at s = u (a,b) inside the torus. What are the forces and torques on the dipole due to the magnetic field? ans (3 pt N = m B; pt N = ŝm f (u); 3 pt F = ( m B); pt F = 0) We have the torque being The magnetic force is N = m B = ŝm f (u) F = ( m B) = 0 d) (15 pt) Suppose the capacitor is made of parallel circular plates each with radius R with vacuum in between. Suppose the charge density on one of the plates for t > 0 is σ(t) and the uniform electric field region between the capaciator plates is then characterized by E σ(t) ẑ. Neglecting the edge effects as usual and assuming rotational symmetry about the axis passing through the center of the plates, find the resulting B φ and the Poynting vector at s = R, somewhere between the parallel plates in the uniform field region. ans (3 pt B = µ 0 E ; pt B φ = µ 0 s σ Since the sign) R s=r = µ 0 σ ; 5 pt S = 1 µ 0 E B s=r ; 5 pt S = ŝ σ(t) B = µ 0 E R σ where one point is for B φ πs = µ 0 πs E z s σ B φ = µ 0 R s=r = µ 0 σ 4
5 Hence, we find As a check, note S = 1 µ 0 E B s=r = ŝ σ(t) R σ which is the energy leaving the uniform field region. πrhs = πrh σ(t) R σ = πrh 1 R σ R E = πrh = = πr h u 3. Suppose you are given that the Maxwell equations were replaced by Ẽ = 0 Ẽ = B L Ẽ B = Ñ Ẽ L Ẽ B = 0 where L and Ñ are complex constants and the tilde indicates that these fields are complex. a) (10 pt) What is the wave equation governing Ẽ? ans (3 pt ( Ẽ) = ( Ẽ) Ẽ; 3 pt Ẽ = 0; 3 pt for substituting B = Ñ Ẽ L Ẽ;1 pt Ẽ = Ñ Ẽ ) Use ( Ẽ) = ( Ẽ) Ẽ Ẽ = ( B + L Ẽ) = (Ñ Ẽ L E + L Ẽ) = Ñ Ẽ b) (10 pt) Find a plane wave solution Ẽ to this Maxwell equation system proportional to e iωt, traveling in the y direction, having a single wavelength, and the boundary condition Ẽ(t = 0, x = 0) = C. Be sure to specify the condition on C coming from the Maxwell equation system. ans (4 pt plane wave form; 3 pt transverse; 3 pt dispersion) Use Ẽ = i( ky ωt) Ce ŷ C = 0 k = ω Ñ k = ω Ñ 5
6 4. (15 pt) A plane wave is incident normal to a dielectric interface as shown: where the index of refraction of medium i {1,} is n i and µ 1 = µ. The incident wave is and the electric field in the rest of the regions can be written as ẼI (t,z) = Ẽ 0I exp[i(k 1 z ωt)] ˆx ẼR (t,z) = Ẽ 0R exp[i( k 1 z ωt)] ˆx ẼT (t,z) = Ẽ 0T exp[i(k z ωt)] ˆx. Recall that one can derive from one of the Maxwell equations the magnetic field for the reflected wave being B(t,z) R = ωµ 1ε 1 Ẽ 0R e i( k 1z ωt)ŷ k 1 where the minus sign in the amplitude comes from the minus sign in k = k 1 ẑ for the reflected wave. Use E continuity and H continuity to find Ẽ 0T just in terms of { Ẽ 0I, n 1, n }. ans (5 pt Ẽ 0I + Ẽ 0R = Ẽ 0T ; 5 pt for ωµ 1ε 1 k 1 Ẽ 0I ωµ 1ε 1 The E boundary condition says while the H boundary condition says k 1 Ẽ 0R = ωµ ε k Ẽ 0R ; 3 pt ω/k i = v i ; pt Ẽ 0T = Ẽ 0I 1+ n n 1 ) Ẽ 0I + Ẽ 0R = Ẽ 0T H (+) = H ( ) Using ω/k i = v i, we find Hence, ωµ 1 ε 1 Ẽ 0I ωµ 1ε 1 Ẽ 0R = ωµ ε k 1 k 1 k 1 v 1 (Ẽ 0I Ẽ 0R ) = 1 v Ẽ 0T Ẽ 0I = (1 + v 1 v )Ẽ 0T Ẽ 0R Ẽ 0T = Ẽ 0I 1 + n n 1 6
7 (extra space) 7
Handout 10: Inductance. Self-Inductance and inductors
1 Handout 10: Inductance Self-Inductance and inductors In Fig. 1, electric current is present in an isolate circuit, setting up magnetic field that causes a magnetic flux through the circuit itself. This
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 informationPhysics 3323, Fall 2014 Problem Set 12 due Nov 21, 2014
Physics 333, Fall 014 Problem Set 1 due Nov 1, 014 Reading: Griffiths Ch. 9.1 9.3.3 1. Square loops Griffiths 7.3 (formerly 7.1). A square loop of wire, of side a lies midway between two long wires, 3a
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 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 information/20 /20 /20 /60. Dr. Galeazzi PHY207 Test #3 November 20, I.D. number:
Signature: Name: I.D. number: You must do ALL the problems Each problem is worth 0 points for a total of 60 points. TO GET CREDIT IN PROBLEMS AND 3 YOU MUST SHOW GOOD WORK. CHECK DISCUSSION SECTION ATTENDED:
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 informationCYK\2009\PH102\Tutorial 10
CYK\2009\PH02\Tutorial 0 Physics II. [G 6.3] Find the force of attraction between two magnetic dipoles, m and m 2, oriented as shown in the Fig., a distance r apart, (a) using F = 2πIRB cos θ, and (b)
More informationApplications of Ampere s Law
Applications of Ampere s Law In electrostatics, the electric field due to any known charge distribution ρ(x, y, z) may alwaysbeobtainedfromthecoulomblaw it sauniversal tool buttheactualcalculation is often
More informationExam 4 Solutions. a. 1,2,and 3 b. 1 and 2, not 3 c. 1 and 3, not 2 d. 2 and 3, not 1 e. only 2
Prof. Darin Acosta Prof. Greg Stewart April 8, 007 1. Which of the following statements is true? 1. In equilibrium all of any excess charge stored on a conductor is on the outer surface.. In equilibrium
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 informationEvaluating this approximately uniform field at the little loop s center which happens to lie on the big loop s axis we find
PHY 35 K. Solutions for problem set #1. Problem 7.: a) We assume the small loop is so much smaller than the big loop or the distance between the loops that the magnetic field of the big loop is approximately
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 informationSecond Year Electromagnetism Summer 2018 Caroline Terquem. Vacation work: Problem set 0. Revisions
Second Year Electromagnetism Summer 2018 Caroline Terquem Vacation work: Problem set 0 Revisions At the start of the second year, you will receive the second part of the Electromagnetism course. This vacation
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 informationProblem 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 informationLouisiana State University Physics 2102, Exam 3, November 11, 2010.
Name: Instructor: Louisiana State University Physics 2102, Exam 3, November 11, 2010. Please be sure to write your name and class instructor above. The test consists of 3 questions (multiple choice), and
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 informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics: Final Exam Review Session Problems Solutions
Department of Physics: 8 Problem 1: Spherical Capacitor 8 Final Exam Review Session Problems Solutions A capacitor consists of two concentric spherical shells The outer radius of the inner shell is a =
More informationLouisiana State University Physics 2102, Exam 3 April 2nd, 2009.
PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),
More informationÜbungen zur Elektrodynamik (T3)
Arnold Sommerfeld Center Ludwig Maximilians Universität München Prof. Dr. vo Sachs SoSe 8 Übungen zur Elektrodynamik T3 Übungsblatt Bearbeitung: Juni - Juli 3, 8 Conservation of Angular Momentum Consider
More informationPhysics 182. Assignment 4
Physics 182 Assignment 4 1. A dipole (electric or magnetic) in a non-uniform field will in general experience a net force. The electric case was the subject of a problem on the midterm exam; here we examine
More informationElectrodynamics I Final Exam - Part A - Closed Book KSU 2005/12/12 Electro Dynamic
Electrodynamics I Final Exam - Part A - Closed Book KSU 2005/12/12 Name Electro Dynamic Instructions: Use SI units. Short answers! No derivations here, just state your responses clearly. 1. (2) Write an
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 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 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 informationChapter 30 Inductance
Chapter 30 Inductance In this chapter we investigate the properties of an inductor in a circuit. There are two kinds of inductance mutual inductance and self-inductance. An inductor is formed by taken
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 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 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 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 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 informationPHYS 110B - HW #4 Spring 2004, Solutions by David Pace Any referenced equations are from Griffiths Problem statements are paraphrased
PHYS 11B - HW #4 Spring 4, Solutions by David Pace Any referenced equations are from Griffiths Problem statements are paraphrased [1.] Problem 8. from Griffiths Reference problem 7.31 figure 7.43. a Let
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 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 informationSUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r.
SUMMARY Phys 53 (University Physics II) Compiled by Prof. Erickson q 1 q Coulomb s Law: F 1 = k e r ˆr where k e = 1 4π =8.9875 10 9 N m /C, and =8.85 10 1 C /(N m )isthepermittivity of free space. Generally,
More information2.1 The electric field outside a charged sphere is the same as for a point source, E(r) =
Chapter Exercises. The electric field outside a charged sphere is the same as for a point source, E(r) Q 4πɛ 0 r, where Q is the charge on the inner surface of radius a. The potential drop is the integral
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 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 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 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 informationMathematical Tripos, Part IB : Electromagnetism
Mathematical Tripos, Part IB : Electromagnetism Proof of the result G = m B Refer to Sec. 3.7, Force and couples, and supply the proof that the couple exerted by a uniform magnetic field B on a plane current
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 informationPhysics 2212 GH Quiz #4 Solutions Spring 2016
Physics 2212 GH Quiz #4 Solutions Spring 2016 I. (18 points) A bar (mass m, length L) is connected to two frictionless vertical conducting rails with loops of wire, in the presence of a uniform magnetic
More informationMassachusetts Institute of Technology Physics 8.03 Practice Final Exam 3
Massachusetts Institute of Technology Physics 8.03 Practice Final Exam 3 Instructions Please write your solutions in the white booklets. We will not grade anything written on the exam copy. This exam is
More informationPhysics 420 Fall 2004 Quiz 1 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers.
Quiz 1 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. A charge q 1 = +5.0 nc is located on the y-axis, 15 µm above the origin, while another charge q
More informationExam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field
Exam 3 Topics Faraday s Law Self Inductance Energy Stored in Inductor/Magnetic Field Circuits LR Circuits Undriven (R)LC Circuits Driven RLC Circuits Displacement Current Poynting Vector NO: B Materials,
More informationECE357H1S 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 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 informationPHYS 408, Optics. Problem Set 1 - Spring Posted: Fri, January 8, 2015 Due: Thu, January 21, 2015.
PHYS 408, Optics Problem Set 1 - Spring 2016 Posted: Fri, January 8, 2015 Due: Thu, January 21, 2015. 1. An electric field in vacuum has the wave equation, Let us consider the solution, 2 E 1 c 2 2 E =
More informationwire, which carries current (a) Find the flux of B through the loop. is pulled to the right at speed v, instead of away?
(b) What is the magnetic force on the bar? In what direction? (c) If the bar starts out with speed vo at time t = 0, and is left to slide, wh later time t? (d) The initial kinetic energy ofthe bar was,
More informationUniversity of California, Berkeley Physics H7B Spring 1999 (Strovink) SOLUTION TO PROBLEM SET 11 Solutions by P. Pebler
University of California Berkeley Physics H7B Spring 999 (Strovink) SOLUTION TO PROBLEM SET Solutions by P. Pebler Purcell 7.2 A solenoid of radius a and length b is located inside a longer solenoid of
More informationPHYS 110B - HW #4 Fall 2005, Solutions by David Pace Equations referenced as EQ. # are from Griffiths Problem statements are paraphrased
PHYS B - HW #4 Fall 5, Solutions by David Pace Equations referenced as EQ. # are from Griffiths Problem statements are paraphrased [.] Problem 8. from Griffiths Reference problem 7.3 figure 7.43. a Let
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 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 informationExam 2 Solutions. Prof. Darin Acosta Prof. Greg Stewart March 27, b 5Ω ->i 1 <- i 2 5Ω. 3V 10Ω 6 V - - i 3 d c 10Ω
PHY49 Spring 6 Exam Solutions Prof. Darin Acosta Prof. Greg Stewart March 7, 6 Exam Solutions a b 5Ω ->i 1
More informationInductance. thevectorpotentialforthemagneticfield, B 1. ] d l 2. 4π I 1. φ 12 M 12 I 1. 1 Definition of Inductance. r 12
Inductance 1 Definition of Inductance When electric potentials are placed on a system of conductors, charges move to cancel the electric field parallel to the conducting surfaces of the conductors. We
More informationInductance and Magnetic Energy
Mutual Inductance Inductance and Magnetic Energy Consider two wire loops or coils. Their geometries can be completely general, and there might be some magnetic materials inside the coils or around them
More informationElectrodynamics Qualifier Examination
Electrodynamics Qualifier Examination January 10, 2007 1. This problem deals with magnetostatics, described by a time-independent magnetic field, produced by a current density which is divergenceless,
More informationPHYS General Physics for Engineering II FIRST MIDTERM
Çankaya University Department of Mathematics and Computer Sciences 2010-2011 Spring Semester PHYS 112 - General Physics for Engineering II FIRST MIDTERM 1) Two fixed particles of charges q 1 = 1.0µC and
More informationChapter 30 INDUCTANCE. Copyright 2012 Pearson Education Inc.
Chapter 30 INDUCTANCE Goals for Chapter 30 To learn how current in one coil can induce an emf in another unconnected coil To relate the induced emf to the rate of change of the current To calculate the
More informationProblem Set 10 Solutions
Massachusetts Institute of Technology Department of Physics Physics 87 Fall 25 Problem Set 1 Solutions Problem 1: EM Waves in a Plasma a Transverse electromagnetic waves have, by definition, E = Taking
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 informationPhysics 1402: Lecture 18 Today s Agenda
Physics 1402: Lecture 18 Today s Agenda Announcements: Midterm 1 distributed available Homework 05 due Friday Magnetism Calculation of Magnetic Field Two ways to calculate the Magnetic Field: iot-savart
More informationPhysics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II
Physics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II In today s lecture, we will discuss generators and motors. Slide 30-1 Announcement Quiz 4 will be next week. The Final
More informationPrinciples of Physics II
Principles of Physics II J. M. Veal, Ph. D. version 18.05.4 Contents 1 Fluid Mechanics 3 1.1 Fluid pressure............................ 3 1. Buoyancy.............................. 3 1.3 Fluid flow..............................
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 informationFIRSTRANKER. 3. (a) Explain scalar magnetic potentialand give its limitations. (b) Explain the importance of vector magnetic potential.
Code No: A109210205 R09 Set No. 2 IIB.Tech I Semester Examinations,MAY 2011 ELECTRO MAGNETIC FIELDS Electrical And Electronics Engineering Time: 3 hours Max Marks: 75 Answer any FIVE Questions All Questions
More informationtoroidal 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 informationFinal Exam Concept Map
Final Exam Concept Map Rule of thumb to study for any comprehensive final exam - start with what you know - look at the quiz problems. If you did not do well on the quizzes, you should certainly learn
More informationExam 3 Review Questions
Exam 3 Review Page 1 of Exam 3 Review Questions 8. Spring 9 Question 1 Which of the following expressions could be a valid representation of the E and B fields in an electromagnetic wave? (Remember that
More informationNIU Ph.D. Candidacy Examination Fall 2017 (8/22/2017) Electricity and Magnetism
NIU Ph.D. Candidacy Examination Fall 2017 (8/22/2017) 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 informationReflection/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 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 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 informationColumbia University Department of Physics QUALIFYING EXAMINATION
Columbia University Department of Physics QUALIFYING EXAMINATION Monday, January 9, 2012 3:10PM to 5:10PM Classical Physics Section 2. Electricity, Magnetism & Electrodynamics Two hours are permitted for
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 information1 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 information2. Waves with higher frequencies travel faster than waves with lower frequencies (True/False)
PHY 2049C Final Exam. Summer 2015. Name: Remember, you know this stuff Answer each questions to the best of your ability. Show ALL of your work (even for multiple choice questions), you may receive partial
More informationELECTROMANETIC PULSE PROPAGATION IN A COAXIAL CABLE
ELECTROMANETIC PULSE PROPAGATION IN A COAXIAL CABLE The mechanical waves on a stretched string are easily generated and observed but not easily studied in quantitative detail. The propagating waves in
More informationGuided waves - Lecture 11
Guided waves - Lecture 11 1 Wave equations in a rectangular wave guide Suppose EM waves are contained within the cavity of a long conducting pipe. To simplify the geometry, consider a pipe of rectangular
More informationExam 2 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses.
Exam 2 Solutions Note that there are several variations of some problems, indicated by choices in parentheses. Problem 1 Part of a long, straight insulated wire carrying current i is bent into a circular
More informationUNIVERSITY OF CALIFORNIA - SANTA CRUZ DEPARTMENT OF PHYSICS PHYS 110A. Homework #7. Benjamin Stahl. March 3, 2015
UNIVERSITY OF CALIFORNIA - SANTA CRUZ DEPARTMENT OF PHYSICS PHYS A Homework #7 Benjamin Stahl March 3, 5 GRIFFITHS, 5.34 It will be shown that the magnetic field of a dipole can written in the following
More informationPHYSICS 7B, Section 1 Fall 2013 Midterm 2, C. Bordel Monday, November 4, pm-9pm. Make sure you show your work!
PHYSICS 7B, Section 1 Fall 2013 Midterm 2, C. Bordel Monday, November 4, 2013 7pm-9pm Make sure you show your work! Problem 1 - Current and Resistivity (20 pts) a) A cable of diameter d carries a current
More information11 Chapter. Inductance and Magnetic Energy
11 Chapter Inductance and Magnetic Energy 11.1 Mutual Inductance... 11-3 Example 11.1 Mutual Inductance of Two Concentric Co-planar Loops... 11-5 11.2 Self-Inductance... 11-6 Example 11.2 Self-Inductance
More informationPreliminary Examination: Electricity and Magnetism Department of Physics and Astronomy University of New Mexico. Fall 2004
Preliminary Examination: Electricity and Magnetism Department of Physics and Astronomy University of New Mexico Fall 2004 Instructions: The exam consists two parts: 5 short answers (6 points each) and
More informationStudent number: Question # Mark Maximum Mark. Multiple Choice 20
Name: Student number: Academic Honesty: Cheating in an examination includes the following: 1. the unauthorized sharing of material such as textbooks during an open book examination; 2. concealing information
More informationPhysics 227 Final Exam Wednesday, May 9, Code: 000
Physics 227 Final Exam Wednesday, May 9, 2018 Physics 227, Section RUID: Code: 000 Your name with exam code Your signature Turn off and put away LL electronic devices NOW. NO cell phones, NO smart watches,
More informationProblem Set 7: Solutions
UNIVERSITY OF ALABAMA Department of Physics and Astronomy PH 126 / LeClair Fall 2009 Problem Set 7: Solutions 1. A thin ring of radius a carries a static charge q. This ring is in a magnetic field of strength
More informationPHY 114 Summer Midterm 2 Solutions
PHY 114 Summer 009 - Midterm Solutions Conceptual Question 1: Can an electric or a magnetic field, each constant in space and time, e used to accomplish the actions descried elow? Explain your answers.
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 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 informationforce per unit length
Physics 153 Sample Examination for Fourth Unit As you should know, this unit covers magnetic fields, how those fields interact with charged particles, how they are produced, how they can produce electric
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 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 information9-3 Inductance. * We likewise can have self inductance, were a timevarying current in a circuit induces an emf voltage within that same circuit!
/3/004 section 9_3 Inductance / 9-3 Inductance Reading Assignment: pp. 90-86 * A transformer is an example of mutual inductance, where a time-varying current in one circuit (i.e., the primary) induces
More informationElectromagnetic Theory PHYS 402. Electrodynamics. Ohm s law Electromotive Force Electromagnetic Induction Maxwell s Equations
Electromagnetic Theory PHYS 4 Electrodynamics Ohm s law Electromotive Force Electromagnetic Induction Maxwell s Equations 1 7.1.1 Ohms Law For the EM force Usually v is small so J = J = σ Current density
More informationCh 30 - Sources of Magnetic Field
Ch 30 - Sources of Magnetic Field Currents produce Magnetism? 1820, Hans Christian Oersted: moving charges produce a magnetic field. The direction of the field is determined using a RHR. Oersted (1820)
More informationExam 2 Solutions. Applying the junction rule: i 1 Applying the loop rule to the left loop (LL), right loop (RL), and the full loop (FL) gives:
PHY61 Eam Solutions 1. [8 points] In the circuit shown, the resistance R 1 = 1Ω. The batter voltages are identical: ε1 = ε = ε3 = 1 V. What is the current (in amps) flowing through the middle branch from
More informationMid Term Exam 3. Apr 24, /40 2 /40 3 /30. Total /110
Name: ID: Mid Term Exam 3 Phys 248 Apr 24, 2009 Print your name and ID number clearly above. To receive full credit you must show all your work. If you do not show your work you will only receive partial
More information