Department of Physics PRELIMINARY EXAMINATION 2015 Part II. Long Questions
|
|
- Bethany Jackson
- 5 years ago
- Views:
Transcription
1 Department of Physics PRELIMINARY EXAMINATION 2015 Part II. Long Questions Friday May 15th, 2014, 14-17h Examiners: Prof. J. Cline, Prof. H. Guo, Prof. G. Gervais (Chair), and Prof. D. Hanna INSTRUCTIONS Answer 4 questions out of the choice of 8. You must attempt one problem in each sub-category, i.e. one in classical mechanics/special relativity, one in quantum mechanics, one in electromagnetic theory and one in statistical mechanics/thermo. This is a closed book exam. Approved calculators may be used (non-programmable ones), though approximate numerical results are valid. If you attempt more than four questions, you should clearly mark which ones should be graded. Write your name and student ID on the exam booklet. question number next to each answer. This exam has 9 pages, including this title page. Clearly indicate the
2 2015 Prelim Long Answers 2 Statistical Mechanics/Thermodynamics The N-atom crystal A cubic crystal contains N atoms. The atoms can exist at lattice sites or an atom may find itself displaced from its normal site into the centre of one of the eight adjacent unit cells. When an atom is displaced, its energy is increased by ɛ > 0 over its energy at the normal lattice site. Suppose that the crystal is in equilibrium at temperature τ. Assume τ ɛ so the chance that two atoms try to occupy the same cell is negligible. We would like you to calculate: (a) the partition function; (b) the entropy; (c) the energy (relative to the energy the crystal would have if all atoms were at their normal sites); (d) the number of atoms in displaced sites. Cereal box A breakfest cereal company puts small toys in its cereal boxes by mixing toys into bulk cereal, and then pouring the mix into boxes. In one production 10,000 boxes contain a total of 15,000 toys. What is the probability that a randomly chosen box will have three toys? You can give your answer as either a number or a formula. Hint! Use the maximum entropy method where S = n p nln(p n ), where p n is the probability that there are n toys in the box. Keep in mind that the system has two constraints and also that the probability of a box having 100 toys is likely to be negligible. 2
3 2015 Prelim Long Answers 3 Quantum Mechanics Beam in a magnetic field Consider a beam of spin polarized electrons moving along the x-direction with velocity v. The spin of the electrons is parallel to the x-axis (see figure below). The beam passes adiabatically into and out of a region 0 < x < L in which there is a small uniform magnetic field B o oriented along the z-axis. Clearly, in the region of the magnetic field, the Hamiltonian of a spin is Ĥ = ge 2mcŜzB o = ω o Ŝ z where Ŝz = ( h/2)σ z is the z-component of the spin operator and σ z its corresponding Pauli matrix. ω o gebo is a constant that depends on the g-factor g, 2mc electron charge e, mass m, speed of light c and the field B o. For this problem, we neglect the orbital part of the Hamiltonian, i.e. we neglect the Lorentz force, etc. (a) What is the normalized spin wave function ψ(x) at x = 0? Note: just before the B o region; we note that the spin is polarized along the x-axis. (b) After a time t, a spin arrives at the position x = L. Determine ψ(x, t) at x = L. Clearly, ψ(x = L, t) = Û(t, 0)ψ(x = 0) where Û = exp[ (i/ h)ĥt] is the time evolution operator. (c) For some strange reason, imagine the original beam splits into two equal beams just before x = 0: one beam passes through the B o region and the other does not. After traversing equal path and maintaining quantum coherence, the two beams are recombined just outside the B o region (i.e. at x = L). What is the wave function of the combined beam there? (d) Following (c), what is the intensity of the recombined beam as a function of B o? Roughly sketch the intensity versus B o and very briefly explain the 3
4 2015 Prelim Long Answers 4 physics indicated by this sketch (Intensity is proportional to ψ(l) 2 ). We provide the Pauli matrices: ( ) ( i σ x =, σ 1 0 y = i 0 ) ( 1 0, σ z = 0 1 ). z Region with uniform magnetic field electron beam B o 0 L X Dipole-dipole interaction. The spin-spin interaction Hamiltonian between two neutrons is ( (1 ) ) V = µ B = µ2 nα( hc) 3 3 (σ (2m p c 2 ) 2 1 σ 2 3 σ 1 ˆr σ 2 ˆr) 8π r 3 σ 1 σ 2 δ 3 (r), where µ n is the magnetic moment in units of nuclear magnetons, (µ n = 1.4 for neutrons), α = 1/137 is the fine structure constant, m p is the proton mass, and the Pauli operators σ i are related to the respective spins of the two neutrons (i = 1, 2) in the usual way, S i = ( h/2)σ i. (a) To estimate the properties of possible bound states of two neutrons, consider the trial wave function ψ(r) = Ne r/a where r is the separation between 4
5 2015 Prelim Long Answers 5 the neutrons. Determine the normalization constant N. What is the angular momentum of this state? (b) Make an order of magnitude estimate of the expectation values of the kinetic and potential energy for the above state, ignoring the mass difference between the proton and the neutron. Assuming V is negative, estimate the magnitude of a that minimizes the total energy, as well as the magnitude of the binding energy. Use hc = 197 MeV fm, m p c 2 = 938 MeV. How do these compare to the size and mass energy of the neutron? Do we expect to see such bound states in nature? (c) Using rotational symmetry, show that the expectation value of V in the above trial state is given by only one of the three terms in V, and calculate it. (d) The result of (c) should depend only upon σ 1 σ 2. Evaluate the latter for the case where the two neutron spins are in the singlet or triplet state of the total spin. Which one leads to bound states? Draw a picture of the spin and dipole magnetic field from one neutron and the spin of the neighboring one to show that your answer agrees with classical expectations for the sign of V in this configuration. (e) Calculate the expectation value of the kinetic energy T. (Notice that reduced mass is relevant here.) Combine with the result of (c) to find the exact estimates for a and for the binding energy. 5
6 2015 Prelim Long Answers 6 Electromagnetic Theory Cylindrical capacitor A cylindrical capacitor of length L consists of an inner conductor wire of radius a, a thin outer conducting shell of radius b. the space in between is filled with nonconducting material of dielectric constant ɛ. (a) Determine the electric field as a function of radial position when the capacitor is charged with total charge Q (you can neglect end effects). (b) Determine the capacitance. (c) Suppose that the dielectric material is pulled part way out of the capacitor while the latter is connected to a battery of potential V. Find the force necessary to hold the dielectric in this position. In which direction must the force be applied? (neglect fringing fields). Polarized sphere A sphere of radius R has a spatially varying permanent polarization P = (R/r) 2 P 0ˆr. It rotates with angular frequency ω around its center. (a) Find the bound charge density on the surface (σ b ) and in the interior (ρ b ). Use Gauss s theorem to prove that ρ b 0. What is the functional form of ρ b? What is the total bound charge of the sphere? (b) Find the electric field inside and outside of the sphere. (c) Find the surface current due to the rotation. Take the axis of rotation to be ẑ. If you can t do it exactly, make an order of magnitude estimate. Check dimensions of your result. 6
7 2015 Prelim Long Answers 7 (d) Find the magnetic moment of the spinning sphere by integrating the contributions from concentric rings of current on the surface. From this, find the magnitude and direction of B at a position z R along the axis of rotation. (If you are not able to compute these exactly, make an order of magnitude estimate.) (e) Using a symmetry argument, describe how the situation [parts (a)-(d)] would differ if the polarization of the sphere was just a constant vector P, parallel to ω. Would there still be a dipole field? 7
8 2015 Prelim Long Answers 8 Classical Mechanics/Special Relativity Relativistic light emitter Consider two frames of reference, S and S. S moves with speed v along the x axis of frame S and its x axis is collinear with the x axis of S. A light beam is emitted at angle θ 0 with respect to the x axis in S. (a) Find the angle θ the beam makes with respect to the x axis in S. (b) A source which radiates light uniformly in all directions in its rest frame radiates strongly in the forward direction in a frame in which it is moving with speed v close to c. Using the result of part (a), find the speed of a source for which half the radiation is emitted in a cone subtending 10 3 rad. The Particle on a hemisphere A particle of mass m starts at rest on top of a smooth fixed hemisphere of radius a (see figure below). We are interested in finding the force of constraint and to determine at which angle the particle will leave the hemisphere as it falls. (a) Show that the Lagrangian is given by L = m 2 (ṙ2 + r 2 θ2 ) mgr cos θ. (b) Determine the equation of constraint f(r, θ) = 0 describing the mass in contact with the hemisphere. (c) Using r and θ as generalized coordinates, write down the Euler-Lagrange equations including the constraint and a single Lagrange multiplier λ. Show that these equations lead to θ = g sin θ. a (d) Show that θ 2 = g cos θ+ g, where the integration constant is g/a because 2 a a θ = 0 at t = 0 when θ = 0. 8
9 2015 Prelim Long Answers 9 Figure 1: The particle on a hemisphere. (e) Using the relation given in part d) show that the Lagrange multiplier is λ = mg(3 cos θ 2) and find at which angles the particle falls off the hemisphere. Show that it is given by θ 0 = cos 1 ( 2 3 ). 9
Department of Physics PRELIMINARY EXAMINATION 2016 Part I. Short Questions
Department of Physics PRELIMINARY EXAMINATION 2016 Part I. Short Questions Thursday May 19th, 2016, 14-17h Examiners: Prof. J. Cline, Prof. H. Guo, Prof. G. Gervais (Chair), and Prof. D. Hanna INSTRUCTIONS
More informationDepartment of Physics PRELIMINARY EXAMINATION 2014 Part II. Long Questions
Department of Physics PRELIMINARY EXAMINATION 2014 Part II. Long Questions Friday May 16th, 2014, 14-17h Examiners: Prof. A. Clerk, Prof. M. Dobbs, Prof. G. Gervais (Chair), Prof. T. Webb, Prof. P. Wiseman
More informationDepartment of Physics PRELIMINARY EXAMINATION 2012 Part II. Long Questions
Department of Physics PRELIMINARY EXAMINATION 2012 Part II. Long Questions Friday May 25th, 2012, 2-5pm INSTRUCTIONS Answer 5 questions out of the choice of 8. This is a closed book exam. Approved calculators
More informationDepartment of Physics PRELIMINARY EXAMINATION 2017 Part II. Long Questions/Answers
Department of Physics PRELIMINARY EXAMINATION 2017 Part II. Long Questions/Answers Friday May 19th, 2017, 14-17h Examiners: Prof. K. Dasgupta, Prof. H. Guo, Prof. G. Gervais (Chair),Prof. D. Hanna, Prof.
More information2011 Ph.D Preliminary Examination
2011 Ph.D Preliminary Examination Part I. Short-questions (Answer 10 out of 16) Instructions: 1. This is a 3-hour close book exam. Approved calculators may be used (non-programmable ones), though approximate
More informationJoint Entrance Examination for Postgraduate Courses in Physics EUF
Joint Entrance Examination for Postgraduate Courses in Physics EUF First Semester/01 Part 1 4 Oct 011 Instructions: DO NOT WRITE YOUR NAME ON THE TEST. It should be identified only by your candidate number
More informationGraduate Written Examination Spring 2014 Part I Thursday, January 16th, :00am to 1:00pm
Graduate Written Examination Spring 2014 Part I Thursday, January 16th, 2014 9:00am to 1:00pm University of Minnesota School of Physics and Astronomy Examination Instructions Part 1 of this exam consists
More information1. Electricity and Magnetism (Fall 1995, Part 1) A metal sphere has a radius R and a charge Q.
1. Electricity and Magnetism (Fall 1995, Part 1) A metal sphere has a radius R and a charge Q. (a) Compute the electric part of the Maxwell stress tensor T ij (r) = 1 {E i E j 12 } 4π E2 δ ij both inside
More informationGraduate Written Examination Fall 2014 Part I
Graduate Written Examination Fall 2014 Part I University of Minnesota School of Physics and Astronomy Aug. 19, 2014 Examination Instructions Part 1 of this exam consists of 10 problems of equal weight.
More informationPreliminary Quantum Questions
Preliminary Quantum Questions Thomas Ouldridge October 01 1. Certain quantities that appear in the theory of hydrogen have wider application in atomic physics: the Bohr radius a 0, the Rydberg constant
More informationPh.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART II. MONDAY, May 5, :00 AM 1:00 PM
Ph.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART II MONDAY, May 5, 2014 9:00 AM 1:00 PM ROOM 245 PHYSICS RESEARCH BUILDING INSTRUCTIONS: This examination consists
More informationψ s a ˆn a s b ˆn b ψ Hint: Because the state is spherically symmetric the answer can depend only on the angle between the two directions.
1. Quantum Mechanics (Fall 2004) Two spin-half particles are in a state with total spin zero. Let ˆn a and ˆn b be unit vectors in two arbitrary directions. Calculate the expectation value of the product
More informationE & M Qualifier. January 11, To insure that the your work is graded correctly you MUST:
E & M Qualifier 1 January 11, 2017 To insure that the your work is graded correctly you MUST: 1. use only the blank answer paper provided, 2. use only the reference material supplied (Schaum s Guides),
More informationPhysics Qual - Statistical Mechanics ( Fall 2016) I. Describe what is meant by: (a) A quasi-static process (b) The second law of thermodynamics (c) A throttling process and the function that is conserved
More informationColumbia University Department of Physics QUALIFYING EXAMINATION
Columbia University Department of Physics QUALIFYING EXAMINATION Friday, January 13, 2012 3:10PM to 5:10PM General Physics (Part II) Section 6. Two hours are permitted for the completion of this section
More informationDepartment of Physics PRELIMINARY EXAMINATION 2014 Part I. Short Questions
Department of Physics PRELIMINARY EXAMINATION 2014 Part I. Short Questions Thursday May 15th, 2014, 14-17h Examiners: Prof. A. Clerk, Prof. M. Dobbs, Prof. G. Gervais (Chair), Prof. T. Webb, Prof. P. Wiseman
More information(a) Write down the total Hamiltonian of this system, including the spin degree of freedom of the electron, but neglecting spin-orbit interactions.
1. Quantum Mechanics (Spring 2007) Consider a hydrogen atom in a weak uniform magnetic field B = Bê z. (a) Write down the total Hamiltonian of this system, including the spin degree of freedom of the electron,
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 informationPh.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART I. FRIDAY, January 3, :00 AM 1:00 PM
Ph.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART I FRIDAY, January 3, 2013 9:00 AM 1:00 PM ROOM 245 PHYSICS RESEARCH BUILDING INSTRUCTIONS: This examination
More informationPhysics PhD Qualifying Examination Part I Wednesday, January 21, 2015
Physics PhD Qualifying Examination Part I Wednesday, January 21, 2015 Name: (please print) Identification Number: STUDENT: Designate the problem numbers that you are handing in for grading in the appropriate
More informationk m Figure 1: Long problem L2 2 + L2 3 I 1
LONG PROBLEMS 1: Consider the system shown in Figure 1: Two objects, of mass m 1 and m, can be treated as point-like. Each of them is suspended from the ceiling by a wire of negligible mass, and of length
More informationM04M.1 Particles on a Line
Part I Mechanics M04M.1 Particles on a Line M04M.1 Particles on a Line Two elastic spherical particles with masses m and M (m M) are constrained to move along a straight line with an elastically reflecting
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 informationMcGill University. Department of Physics. Ph.D. Preliminary Examination. Long Questions
McGill University Department of Physics Ph.D. Preliminary Examination Long Questions Examiners: Date: Tuesday May 27, 2003 Time: 2:00 p.m. to 5:00 p.m. C. Burgess (Chairman) S. Das Gupta V. Kaspi J. Strom
More informationQualifying Exam. Aug Part II. Please use blank paper for your work do not write on problems sheets!
Qualifying Exam Aug. 2015 Part II Please use blank paper for your work do not write on problems sheets! Solve only one problem from each of the four sections Mechanics, Quantum Mechanics, Statistical Physics
More informationSpring 2007 Qualifier- Part I 7-minute Questions
Spring 007 Qualifier- Part I 7-minute Questions 1. Calculate the magnetic induction B in the gap of a C-shaped iron core electromagnet wound with n turns of a wire carrying current I as shown in the figure.
More informationColumbia University Department of Physics QUALIFYING EXAMINATION
Columbia University Department of Physics QUALIFYING EXAMINATION Monday, January 14, 2013 3:10PM to 5:10PM Classical Physics Section 2. Electricity, Magnetism & Electrodynamics Two hours are permitted
More informationand another with a peak frequency ω 2
Physics Qualifying Examination Part I 7-Minute Questions September 13, 2014 1. A sealed container is divided into two volumes by a moveable piston. There are N A molecules on one side and N B molecules
More informationJ10M.1 - Rod on a Rail (M93M.2)
Part I - Mechanics J10M.1 - Rod on a Rail (M93M.2) J10M.1 - Rod on a Rail (M93M.2) s α l θ g z x A uniform rod of length l and mass m moves in the x-z plane. One end of the rod is suspended from a straight
More informationDEPARTMENT OF PHYSICS. University at Albany State University of New York. Comprehensive Field Examination. Classical. Monday, May 21, 2018
DEPARTMENT OF PHYSICS University at Albany State University of New York Comprehensive Field Examination Classical Monday, May 21, 218 1: AM - 1: PM Instruction: Answer any four out of five questions Please
More information(a) What are the probabilities associated with finding the different allowed values of the z-component of the spin after time T?
1. Quantum Mechanics (Fall 2002) A Stern-Gerlach apparatus is adjusted so that the z-component of the spin of an electron (spin-1/2) transmitted through it is /2. A uniform magnetic field in the x-direction
More informationUNIVERSITY OF MISSOURI-COLUMBIA PHYSICS DEPARTMENT. PART I Qualifying Examination. January 20, 2015, 5:00 p.m. to 8:00 p.m.
UNIVERSITY OF MISSOURI-COLUMBIA PHYSICS DEPARTMENT PART I Qualifying Examination January 20, 2015, 5:00 p.m. to 8:00 p.m. Instructions: The only material you are allowed in the examination room is a writing
More information(relativistic effects kinetic energy & spin-orbit coupling) 3. Hyperfine structure: ) (spin-spin coupling of e & p + magnetic moments) 4.
4 Time-ind. Perturbation Theory II We said we solved the Hydrogen atom exactly, but we lied. There are a number of physical effects our solution of the Hamiltonian H = p /m e /r left out. We already said
More informationQUALIFYING EXAMINATION, Part 1. 2:00 PM 5:00 PM, Thursday September 3, 2009
QUALIFYING EXAMINATION, Part 1 2:00 PM 5:00 PM, Thursday September 3, 2009 Attempt all parts of all four problems. Please begin your answer to each problem on a separate sheet, write your 3 digit code
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 informationPRELIMINARY EXAMINATION Department of Physics University of Florida Part A, January, 2012, 09:00 12:00. Instructions
Student ID Number: PRELIMINARY EXAMINATION Part A, January, 2012, 09:00 12:00 Instructions 1. You may use a calculator and CRC Math tables or equivalent. No other tables or aids are allowed or required.
More informationJoint Entrance Examination for Postgraduate Courses in Physics EUF
Joint Entrance Examination for Postgraduate Courses in Physics EUF For the first semester 2014 Part 1 15 October 2013 Instructions: DO NOT WRITE YOUR NAME ON THE TEST. It should be identified only by your
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 informationReview. Spring Semester /21/14. Physics for Scientists & Engineers 2 1
Review Spring Semester 2014 Physics for Scientists & Engineers 2 1 Notes! Homework set 13 extended to Tuesday, 4/22! Remember to fill out SIRS form: https://sirsonline.msu.edu Physics for Scientists &
More informationM02M.1 Particle in a Cone
Part I Mechanics M02M.1 Particle in a Cone M02M.1 Particle in a Cone A small particle of mass m is constrained to slide, without friction, on the inside of a circular cone whose vertex is at the origin
More informationPhysics Graduate Group. Saturday, September 15 th 2007
UNIVERSITY OF CALIFORNIA, MERCED Physics Graduate Group Saturday, September 15 th 2007 9:00 am 1:00 pm Instructions: 1 SHOW ALL WORK. 2 This is a closed book exam. 3 Do all eight (8) problems. 4 You have
More informationSection B. Electromagnetism
Prelims EM Spring 2014 1 Section B. Electromagnetism Problem 0, Page 1. An infinite cylinder of radius R oriented parallel to the z-axis has uniform magnetization parallel to the x-axis, M = m 0ˆx. Calculate
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 informationDepartment of Physics, Princeton University. Graduate Preliminary Examination Part I. Thursday, May 7, :00 am - 12:00 noon
Department of Physics, Princeton University Graduate Preliminary Examination Part I Thursday, May 7, 2015 9:00 am - 12:00 noon Answer TWO out of the THREE questions in Section A (Mechanics) and TWO out
More informationMechanics and Statistical Mechanics Qualifying Exam Spring 2006
Mechanics and Statistical Mechanics Qualifying Exam Spring 2006 1 Problem 1: (10 Points) Identical objects of equal mass, m, are hung on identical springs of constant k. When these objects are displaced
More informationINSTRUCTIONS PART I : SPRING 2006 PHYSICS DEPARTMENT EXAM
INSTRUCTIONS PART I : SPRING 2006 PHYSICS DEPARTMENT EXAM Please take a few minutes to read through all problems before starting the exam. Ask the proctor if you are uncertain about the meaning of any
More informationJoint Entrance Examination for Postgraduate Courses in Physics EUF
Joint Entrance Examination for Postgraduate Courses in Physics EUF Second Semester 013 Part 1 3 April 013 Instructions: DO NOT WRITE YOUR NAME ON THE TEST. It should be identified only by your candidate
More informationDEPARTMENT OF PHYSICS BROWN UNIVERSITY Written Qualifying Examination for the Ph.D. Degree January 23, 2009 READ THESE INSTRUCTIONS CAREFULLY
DEPARTMENT OF PHYSICS BROWN UNIVERSITY Written Qualifying Examination for the Ph.D. Degree January 23, 2009 READ THESE INSTRUCTIONS CAREFULLY 1. The time allowed to complete the exam is 12:00 5:00 PM.
More informationElectrodynamics Qualifier Examination
Electrodynamics Qualifier Examination August 15, 2007 General Instructions: In all cases, be sure to state your system of units. Show all your work, write only on one side of the designated paper, and
More informationJ07M.1 - Ball on a Turntable
Part I - Mechanics J07M.1 - Ball on a Turntable J07M.1 - Ball on a Turntable ẑ Ω A spherically symmetric ball of mass m, moment of inertia I about any axis through its center, and radius a, rolls without
More informationSAMPLE PAPER-05 (solved) PHYSICS (Theory) Class XII. Time allowed: 3 hours Marks: 70
SAMPLE PAPER-05 (solved) PHYSICS (Theory) Class XII Time allowed: 3 hours Marks: 70 Maximum General Instructions: a) All the questions are compulsory. b) There are 26 questions in total. c) Questions 1
More informationElectricity & Magnetism Qualifier
Electricity & Magnetism Qualifier For each problem state what system of units you are using. 1. Imagine that a spherical balloon is being filled with a charged gas in such a way that the rate of charge
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 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 informationEUF. Joint Entrance Examination for Postgraduate Courses in Physics
EUF Joint Entrance Examination for Postgraduate Courses in Physics For the second semester 2015 14 April 2015 Part 1 Instructions Do not write your name on the test. It should be identified only by your
More informationPh.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART I. FRIDAY, May 5, :00 12:00
Ph.D. QUALIFYING EXAMINATION DEPARTMENT OF PHYSICS AND ASTRONOMY WAYNE STATE UNIVERSITY PART I FRIDAY, May 5, 2017 10:00 12:00 ROOM 245 PHYSICS RESEARCH BUILDING INSTRUCTIONS: This examination consists
More informationFinal Exam - Solutions PHYS/ECE Fall 2011
Final Exam - Solutions PHYS/ECE 34 - Fall 211 Problem 1 Cosmic Rays The telescope array project in Millard County, UT can detect cosmic rays with energies up to E 1 2 ev. The cosmic rays are of unknown
More information(a) Sections 3.7 through (b) Sections 8.1 through 8.3. and Sections 8.5 through 8.6. Problem Set 4 due Monday, 10/14/02
Physics 601 Dr. Dragt Fall 2002 Reading Assignment #4: 1. Dragt (a) Sections 1.5 and 1.6 of Chapter 1 (Introductory Concepts). (b) Notes VI, Hamilton s Equations of Motion (to be found right after the
More information- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
- 5 - TEST 2 This test is on the final sections of this session's syllabus and should be attempted by all students. QUESTION 1 [Marks 23] A thin non-conducting rod is bent to form the arc of a circle of
More informationUNIVERSITY OF MISSOURI-COLUMBIA PHYSICS DEPARTMENT. PART I Qualifying Examination. August 20, 2013, 5:00 p.m. to 8:00 p.m.
UNIVERSITY OF MISSOURI-COLUMBIA PHYSICS DEPARTMENT PART I Qualifying Examination August 20, 2013, 5:00 p.m. to 8:00 p.m. Instructions: The only material you are allowed in the examination room is a writing
More informationPhysical Dynamics (SPA5304) Lecture Plan 2018
Physical Dynamics (SPA5304) Lecture Plan 2018 The numbers on the left margin are approximate lecture numbers. Items in gray are not covered this year 1 Advanced Review of Newtonian Mechanics 1.1 One Particle
More informationUniversity of Michigan Physics Department Graduate Qualifying Examination
Name: University of Michigan Physics Department Graduate Qualifying Examination Part II: Modern Physics Saturday 17 May 2014 9:30 am 2:30 pm Exam Number: This is a closed book exam, but a number of useful
More informationPhysics 221A Fall 1996 Notes 13 Spins in Magnetic Fields
Physics 221A Fall 1996 Notes 13 Spins in Magnetic Fields A nice illustration of rotation operator methods which is also important physically is the problem of spins in magnetic fields. The earliest experiments
More informationGRADUATE WRITTEN EXAMINATION. Fall 2018 PART I
University of Minnesota School of Physics and Astronomy GRADUATE WRITTEN EXAMINATION Fall 2018 PART I Monday, August 20 th, 2018 9:00 am to 1:00 pm Part 1 of this exam consists of 10 problems of equal
More informationPhysics 106a, Caltech 4 December, Lecture 18: Examples on Rigid Body Dynamics. Rotating rectangle. Heavy symmetric top
Physics 106a, Caltech 4 December, 2018 Lecture 18: Examples on Rigid Body Dynamics I go through a number of examples illustrating the methods of solving rigid body dynamics. In most cases, the problem
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 informationPhysics 222, Spring 2010 Quiz 3, Form: A
Physics 222, Spring 2010 Quiz 3, Form: A Name: Date: Instructions You must sketch correct pictures and vectors, you must show all calculations, and you must explain all answers for full credit. Neatness
More informationQualifying Exam for Ph.D. Candidacy Department of Physics October 11, 2014 Part I
Qualifying Exam for Ph.D. Candidacy Department of Physics October 11, 214 Part I Instructions: The following problems are intended to probe your understanding of basic physical principles. When answering
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 PhD Qualifying Examination Part I Wednesday, August 26, 2015
Physics PhD Qualifying Examination Part I Wednesday, August 26, 2015 Name: (please print) Identification Number: STUDENT: Designate the problem numbers that you are handing in for grading in the appropriate
More information(a) Consider a sphere of charge with radius a and charge density ρ(r) that varies with radius as. ρ(r) = Ar n for r a
Physics 7B Midterm 2 - Fall 207 Professor R. Birgeneau Total Points: 00 ( Problems) This exam is out of 00 points. Show all your work and take particular care to explain your steps. Partial credit will
More informationTHE UNIVERSITY OF PRETORIA
PHY 255 THE UNIVERSITY OF PRETORIA FIRST SEMESTER, 2011 Campus: Hatfield PHYSICS 255 Modern Physics Exam Total: 70 (Time allowed: THREE hours Internal Examiner: M. van den Worm External Examiner: Q. Odendaal
More informationM01M.1 Massive Spring
Part I Mechanics M01M.1 Massive Spring M01M.1 Massive Spring A spring has spring constant K, unstretched length L, and mass per unit length ρ. The spring is suspended vertically from one end in a constant
More informationPHYSICAL SCIENCES PART A
PHYSICAL SCIENCES PART A 1. The calculation of the probability of excitation of an atom originally in the ground state to an excited state, involves the contour integral iωt τ e dt ( t τ ) + Evaluate the
More informationCommon Exam Department of Physics University of Utah August 24, 2002
Common Exam - 2002 Department of Physics University of Utah August 24, 2002 Examination booklets have been provided for recording your work and your solutions. Please note that there is a separate booklet
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF PHYSICS. DOCTORAL GENERAL EXAMINATION PART 1 August 27, 2012 FIVE HOURS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF PHYSICS EDUCATION OFFICE PHONE (617)-253-4842 ROOM 4-352 FAX (617)-258-8319 DOCTORAL GENERAL EXAMINATION PART 1 August 27, 2012 FIVE HOURS 1. This examination
More informationPH Physics 211 Exam-2
PH 211 724214 Physics 211 Exam2 NAME: Write down your name also on the back of your exam. SIGNATURE and ID: Write down your name on the back of the package of sheets you turn in. Notice: The exam is worth
More informationFinal Exam: Physics Spring, 2017 May 8, 2017 Version 01
Final Exam: Physics2331 - Spring, 2017 May 8, 2017 Version 01 NAME (Please Print) Your exam should have 11 pages. This exam consists of 18 multiple-choice questions (2 points each, worth 36 points), and
More informationPh.D. QUALIFYING EXAMINATION PART A. Tuesday, January 3, 2012, 1:00 5:00 P.M.
PhD QUALIFYING EXAMINATION PART A Tuesday, January 3, 212, 1: 5: PM Work each problem on a separate sheet(s) of paper and put your identifying number on each page Do not use your name Each problem has
More informationElectrodynamics Exam Solutions
Electrodynamics Exam Solutions Name: FS 215 Prof. C. Anastasiou Student number: Exercise 1 2 3 4 Total Max. points 15 15 15 15 6 Points Visum 1 Visum 2 The exam lasts 18 minutes. Start every new exercise
More informationPhysics 208 Final Exam May 12, 2008
Page 1 Name: Solutions Student ID: Section #: Physics 208 Final Exam May 12, 2008 Print your name and section clearly above. If you do not know your section number, write your TA s name. Your final answer
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 informationAtomic Structure. Chapter 8
Atomic Structure Chapter 8 Overview To understand atomic structure requires understanding a special aspect of the electron - spin and its related magnetism - and properties of a collection of identical
More informationGraduate Preliminary Examination, Thursday, January 6, Part I 2
Graduate Preliminary Examination, Thursday, January 6, 2011 - Part I 2 Section A. Mechanics 1. ( Lasso) Picture from: The Lasso: a rational guide... c 1995 Carey D. Bunks A lasso is a rope of linear mass
More informationUniversity of Michigan Physics Department Graduate Qualifying Examination
Name: University of Michigan Physics Department Graduate Qualifying Examination Part I: Classical Physics Saturday 10 January 2015 9:30 am 2:30 pm Exam Number: This is a closed book exam, but a number
More informationAngular momentum and spin
Luleå tekniska universitet Avdelningen för Fysik, 007 Hans Weber Angular momentum and spin Angular momentum is a measure of how much rotation there is in particle or in a rigid body. In quantum mechanics
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 informationPhysics 208 Final Exam December 15, 2008
Page 1 Name: Student ID: Section #: Physics 208 Final Exam December 15, 2008 Print your name and section clearly above. If you do not know your section number, write your TA s name. Your final answer must
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 informationAtomic Structure and Atomic Spectra
Atomic Structure and Atomic Spectra Atomic Structure: Hydrogenic Atom Reading: Atkins, Ch. 10 (7 판 Ch. 13) The principles of quantum mechanics internal structure of atoms 1. Hydrogenic atom: one electron
More informationSpring 2012 Qualifying Exam. Part I
Spring 2012 Qualifying Exam Part I Calculators are allowed. No reference material may be used. Please clearly mark the problems you have solved and want to be graded. Mark exactly eight problems in section
More informationSTONY BROOK UNIVERSITY DEPARTMENT OF PHYSICS AND ASTRONOMY. Comprehensive Examination. Classical Mechanics. August 25, 2014
STONY BROOK UNIVERSITY DEPARTMENT OF PHYSICS AND ASTRONOMY Comprehensive Examination Classical Mechanics August 25, 2014 General Instructions: Three problems are given. If you take this exam as a placement
More informationPhysics (
Question 2.12: A charge of 8 mc is located at the origin. Calculate the work done in taking a small charge of 2 10 9 C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).
More information2008 Ph.D Preliminary Examination
008 Ph.D Preliminary Examination Part I. Short-questions (Answer 0 out of 5) Instructions:. This is a 3-hour close book exam. Approved calculators may be used (non-programmable ones), though approximate
More information2m 2 Ze2. , where δ. ) 2 l,n is the quantum defect (of order one but larger
PHYS 402, Atomic and Molecular Physics Spring 2017, final exam, solutions 1. Hydrogenic atom energies: Consider a hydrogenic atom or ion with nuclear charge Z and the usual quantum states φ nlm. (a) (2
More informationIndiana University Physics P331: Theory of Electromagnetism Review Problems #3
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
More informationCandidacy Exam Department of Physics February 6, 2010 Part I
Candidacy Exam Department of Physics February 6, 2010 Part I Instructions: ˆ The following problems are intended to probe your understanding of basic physical principles. When answering each question,
More informationNYU Physics Preliminary Examination in Electricity & Magnetism Fall 2011
This is a closed-book exam. No reference materials of any sort are permitted. Full credit will be given for complete solutions to the following five questions. 1. An impenetrable sphere of radius a carries
More informationJ09M.1 - Coupled Pendula
Part I - Mechanics J09M.1 - Coupled Pendula J09M.1 - Coupled Pendula Two simple pendula, each of length l and mass m, are coupled by a spring of force constant k. The spring is attached to the rods of
More informationHW3 Physics 311 Mechanics
HW3 Physics 311 Mechanics FA L L 2 0 1 5 P H Y S I C S D E PA R T M E N T U N I V E R S I T Y O F W I S C O N S I N, M A D I S O N I N S T R U C T O R : P R O F E S S O R S T E F A N W E S T E R H O F
More information