Electromagnetism  Lecture 10. Magnetic Materials

 Isabella Hodges
 6 months ago
 Views:
Transcription
1 Electromagnetism  Lecture 10 Magnetic Materials Magnetization Vector M Magnetic Field Vectors B and H Magnetic Susceptibility & Relative Permeability Diamagnetism Paramagnetism Effects of Magnetic Materials 1
2 Introduction to Magnetic Materials There are three main types of magnetic materials with different magnetic susceptibilities, χ M : Diamagnetic  magnetization is opposite to external B χ M is small and negative. Paramagnetic  magnetization is parallel to external B χ M is small and positive. Ferromagnetic  magnetization is very large and nonlinear. χ M is large and variable. Can form permanent magnets in absence of external B In this lecture Diamagnetism & Paramagnetism Ferromagnetism will be discussed in Lecture 12 2
3 Magnetization Vector The magnetic dipole moment of an atom can be expressed as an integral over the electron orbits in the Bohr model: m = IAẑ atom The current and magnetic moment of the ith electron are: I = ev i 2πr i m i = IAẑ = e 2m e L i The magnetic dipole density is the magnetization vector M: M = dm dτ = N e A < L i > atom 2m e This orbital angular momentum average is also valid in quantum mechanics 3
4 Notes: Diagrams: 4
5 Magnetization Currents The magnetization vector M has units of A/m The magnetization can be thought of as being produced by a magnetization current density J M : M.dl = J M.dS J M = M L A For a rod uniformly magnetized along its length the magnetization can be represented by a surface magnetization current flowing round the rod: J S = M ˆn The distributions J M and J S represent the effect of the atomic magnetization with equivalent macroscopic current distributions 5
6 Magnetic Field Vectors Ampère s Law is modified to include magnetization effects: B.dl = µ 0 (J C + J M ).ds B = µ 0 (J C + J M ) L A where J C are conduction currents (if any) Using M = J M this can be rewritten as: (B µ 0 M) = µ 0 J C H = J C H = B µ 0 M B is known as the magnetic flux density in Tesla H is known as the magnetic field strength in A/m Ampère s Law in terms of H is: H.dl = J C.dS L A H = J C 6
7 Notes: Diagrams: 7
8 Relative Permeability The magnetization vector is proportional to the external magnetic field strength H: M = χ M H where χ M is the magnetic susceptibility of the material Note  some books use χ B = µ 0 M/B instead of χ M = M/H The linear relationship between B, H and M: B = µ 0 (H + M) can be expressed in terms of a relative permeability µ r B = µ r µ 0 H µ r = 1 + χ M General advice  wherever µ 0 appears in electromagnetism, it should be replaced by µ r µ 0 for magnetic materials 8
9 Diamagnetism For atoms or molecules with even numbers of electrons the orbital angular momentum states +L z and L z are paired and there is no net magnetic moment in the absence of an external field An external magnetic field B z changes the angular velocities: ω = ω ω ω = eb z 2m e where ω is known as the Larmor precession frequency Can think of as effect of magnetic force, or as example of induction For an electron pair in an external B z, the electron with +L z has ω = ω ω, and the electron with L z has ω = ω + ω For both electrons magnetic dipole moment changes in z direction! 9
10 Diamagnetic Magnetization Change in orbital angular momentum of electron pair due to Larmor precession frequency: L z = 2m e r 2 ω = eb z r 2 and the induced magnetic moment of the pair: m = e 2m e L z ẑ = e2 2m e B z r 2 ẑ Averaging over all electron orbits introduces a geometric factor 1/3: M = N A α M B = N Ae 2 Z < r 2 > B 6m e where the atomic magnetic susceptibility is small and negative: α M = e2 Z < r 2 > 6m e Z 10
11 Notes: Diagrams: 11
12 Notes: Diagrams: 12
13 Paramagnetism Paramagnetic materials have atoms or molecules with a net magnetic moment which tends to align with an external field Atoms with odd numbers of electrons have the magnetic moment of the unpaired electron: m = e L 2m e Ions and some ionic molecules have magnetic moments associated with the valence electrons Metals have a magnetization associated with the spins of the conduction electrons near the Fermi surface: M = 3N eµ 2 B 2kT F B ɛ F = kt F 10eV where µ B = e h/2m e is the Bohr magneton 13
14 Susceptibility of Paramagnetic Materials The alignment of the magnetic dipoles with the external field is disrupted by thermal motion: N(θ)dθ e U/kT sin θdθ U = m.b = mb cos θ Expanding the exponent under the assumption that U kt : M = N A m 2 3kT Paramagnetic susceptibility χ M is small and positive. It decreases with increasing temperature: ( ) m 2 χ M = N A 3kT α M where the second term is the atomic susceptibility from the diamagnetism of the paired electrons. B 14
15 Energy Storage in Magnetic Materials The inductance of a solenoid increases if the solenoid is filled with a paramagnetic material: L = µ r µ 0 n 2 πa 2 l = µ r L 0 Hence the energy stored in the solenoid increases: U = 1 2 LI2 = µ r U 0 The energy density of the magnetic field becomes: du M dτ = 1 2 B 2 µ r µ 0 = 1 2 B.H These are HUGE effects for ferromagnetic materials 15
16 Notes: Diagrams: 16
Electromagnetism  Lecture 12. Ferromagnetism & Superconductivity
Electromagnetism  Lecture 12 Ferromagnetism & Superconductivity Ferromagnetism Hysteresis & Permanent Magnets Ferromagnetic Surfaces Toroid with Ferromagnetic Core Superconductivity The Meissner Effect
More informationPhysics of Magnetism. Chapter references are to Essentials of Paleomagnetism, UC Press, 2010
Physics of Magnetism Chapter references are to Essentials of Paleomagnetism, UC Press, 2010 http://magician.ucsd.edu/essentials 1 Magnetic units (sorry!) SI cgs Magnetic fields as the gradient of a scalar
More informationPHY331 Magnetism. Lecture 3
PHY331 Magnetism Lecture 3 Last week Derived magnetic dipole moment of a circulating electron. Discussed motion of a magnetic dipole in a constant magnetic field. Showed that it precesses with a frequency
More informationPhysics 202, Lecture 14
Physics 202, Lecture 14 Today s Topics Sources of the Magnetic Field (Ch. 30) Review: iotsavart Law, Ampere s Law Displacement Current: AmpereMaxwell Law Magnetism in Matter Maxwell s Equations (prelude)
More informationMagnetic Materials. 1. Magnetization 2. Potential and field of a magnetized object
Magnetic Materials 1. Magnetization 2. Potential and field of a magnetized object 3. Hfield 4. Susceptibility and permeability 5. Boundary conditions 6. Magnetic field energy and magnetic pressure 1 Magnetic
More informationCoaxial cable. Coaxial cable. Magnetic field inside a solenoid
Divergence and circulation Surface S Ampere s Law A vector field is generally characterized by 1) how field lines possibly diverge away from or converge upon (point) sources plus 2) how field lines circulate,
More informationDisplacement Current. Ampere s law in the original form is valid only if any electric fields present are constant in time
Displacement Current Ampere s law in the original form is valid only if any electric fields present are constant in time Maxwell modified the law to include timesaving electric fields Maxwell added an
More informationLinear and Nonlinear Magnetic Media (Griffiths Chapter 6: Sections 34) Auxiliary Field H We write the total current density flowing through matter as
Dr. Alain Brizard Electromagnetic Theory I (PY 02) Linear and Nonlinear Magnetic Media (Griffiths Chapter 6: Sections 4) Auxiliary Field H We write the total current density flowing through matter as
More information1 CHAPTER 12 PROPERTIES OF MAGNETIC MATERIALS
1 CHAPTER 12 PROPERTIES OF MAGNETIC MATERIALS 12.1 Introduction This chapter is likely to be a short one, not least because it is a subject in which my own knowledge is, to put it charitably, a little
More informationChapter 28 Magnetic Fields Sources
Chapter 28 Magnetic Fields Sources All known magnetic sources are due to magnetic dipoles and inherently macroscopic current sources or microscopic spins and magnetic moments Goals for Chapter 28 Study
More informationUNIT  IV SEMICONDUCTORS AND MAGNETIC MATERIALS
1. What is intrinsic If a semiconductor is sufficiently pure, then it is known as intrinsic semiconductor. ex:: pure Ge, pure Si 2. Mention the expression for intrinsic carrier concentration of intrinsic
More informationLecture 19: Magnetic properties and the Nephelauxetic effect
Lecture 19: Magnetic properties and the Nephelauxetic effect sample balance thermometer connection to balance left: the Gouy balance for Gouy Tube determining the magnetic susceptibility of materials north
More informationMagnetic Force on a Moving Charge
Magnetic Force on a Moving Charge Electric charges moving in a magnetic field experience a force due to the magnetic field. Given a charge Q moving with velocity u in a magnetic flux density B, the vector
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 informationMn(acetylacetonate) 3. Synthesis & Characterization
Mn(acetylacetonate) 3 Synthesis & Characterization The acac Ligand Acetylacetonate (acac) is a bidentate anionic ligand ( 1 charge). We start with acetylacetone (or Hacac) which has the IUPAC name 2,4
More informationDef.: Magnetism the property of a material to be attracted to (paramagnetic response) or repelled by (diamagnetic response) a magnetic field
5.2 Magnetism: the basics Def.: Magnetism the property of a material to be attracted to (paramagnetic response) or repelled by (diamagnetic response) a magnetic field These effects arise mainly from electrons
More informationCurrent Loop as a Magnetic Dipole & Dipole Moment:
MAGNETISM 1. Bar Magnet and its properties 2. Current Loop as a Magnetic Dipole and Dipole Moment 3. Current Solenoid equivalent to Bar Magnet 4. Bar Magnet and it Dipole Moment 5. Coulomb s Law in Magnetism
More informationphysics 590 ruslan prozorov magnetic measurements Nov 9,
physics 590 ruslan prozorov magnetic measurements Nov 9, 2009  magnetic moment of free currents Magnetic moment of a closed loop carrying current I: Magnetic field on the axis of a loop of radius R at
More informationChapter 29: Magnetic Fields Due to Currents. PHY2049: Chapter 29 1
Chapter 29: Magnetic Fields Due to Currents PHY2049: Chapter 29 1 Law of Magnetism Unlike the law of static electricity, comes in two pieces Piece 1: Effect of B field on moving charge r r F = qv B (Chapt.
More informationThe Spin (continued). February 8, 2012
The Spin continued. Magnetic moment of an electron Particle wave functions including spin SternGerlach experiment February 8, 2012 1 Magnetic moment of an electron. The coordinates of a particle include
More informationAn introduction to magnetism in three parts
An introduction to magnetism in three parts Wulf Wulfhekel Physikalisches Institut, Karlsruhe Institute of Technology (KIT) Wolfgang Gaede Str. 1, D76131 Karlsruhe 0. Overview Chapters of the three lectures
More informationThe Oxford Solid State Basics
The Oxford Solid State Basics Steven H. Simon University of Oxford OXFORD UNIVERSITY PRESS Contents 1 About Condensed Matter Physics 1 1.1 What Is Condensed Matter Physics 1 1.2 Why Do We Study Condensed
More informationV27: RF Spectroscopy
MartinLutherUniversität HalleWittenberg FB Physik Advanced Lab Course V27: RF Spectroscopy ) Electron spin resonance (ESR) Investigate the resonance behaviour of two coupled LC circuits (an active rf
More informationLecture Presentation. Chapter 10 Chemical Bonding II: Molecular Shapes, Valence Bond Theory, and Molecular Orbital Theory
Lecture Presentation Chapter 10 Chemical Bonding II: Molecular Shapes, Valence Bond Theory, and Molecular Orbital Theory Predicting Molecular Geometry 1. Draw the Lewis structure. 2. Determine the number
More informationMagnetic Moments and Spin
Magnetic Moments and Spin Still have several Homeworks to hand back Finish up comments about hydrogen atom and start on magnetic moment + spin. Eleventh Homework Set is due today and the last one has been
More informationLecture 24 Origins of Magnetization (A number of illustrations in this lecture were generously provided by Prof. Geoffrey Beach)
Lecture 4 Origins of Magnetization (A number of illustrations in this lecture were generously provided by Prof. Geoffrey Beach) Today 1. Magnetic dipoles.. Orbital and spin angular momenta. 3. Noninteracting
More informationAtoms, Molecules and Solids (selected topics)
Atoms, Molecules and Solids (selected topics) Part I: Electronic configurations and transitions Transitions between atomic states (Hydrogen atom) Transition probabilities are different depending on the
More informationCHARGED PARTICLE MOTION IN CONSTANT AND UNIFORM ELECTROMAGNETIC FIELDS
CHARGED PARTICLE MOTION IN CONSTANT AND UNIFORM ELECTROMAGNETIC FIELDS In this and in the following two chapters we investigate the motion of charged particles in the presence of electric and magnetic
More informationProblems in Magnetic Properties of Materials
Problems in Magnetic Properties of Materials Notations used: H: Magnetic field stregth B: Magnetic flux density I: Intensity of Magentization (Please note that, in text book, notation, M, is used for Intensity
More informationZeeman Effect  Lab exercises 24
Zeeman Effect  Lab exercises 24 Pieter Zeeman Franziska Beyer August 2010 1 Overview and Introduction The Zeeman effect consists of the splitting of energy levels of atoms if they are situated in a magnetic
More informationExperiment 33 THE STERNGERLACH EXPERIMENT. Theory: A Quantum Magnetic Dipole in an External Field 2. The SternGerlach Apparatus 5
33i Experiment 33 THE STERNGERLACH EXPERIMENT Introduction 1 Theory: A Quantum Magnetic Dipole in an External Field 2 The SternGerlach Apparatus 5 Deflection of Atoms in the Beam 7 Procedure 9 Analysis
More informationMAGNETIC DIPOLES, HYSTERESIS AND CORE LOSES
Power Quality For The Digital Age MAGNETIC DIPOLES, HYSTERESIS AND CORE LOSES A N E N V I R O N M E N T A L P O T E N T I A L S W H I T E P A P E R By Professor Edward Price Director of Research and Development
More informationTypes of Magnetism and Magnetic Domains
Types of Magnetism and Magnetic Domains Magnets or objects with a Magnetic Moment A magnet is an object or material that attracts certain metals, such as iron, nickel and cobalt. It can also attract or
More informationMagnetic domain theory in dynamics
Chapter 3 Magnetic domain theory in dynamics Microscale magnetization reversal dynamics is one of the hot issues, because of a great demand for fast response and high density data storage devices, for
More informationTopics. The concept of spin Precession of magnetic spin Relaxation Bloch Equation. Bioengineering 280A Principles of Biomedical Imaging
Bioengineering 280A Principles of Biomedical Imaging Fall Quarter 2006 MRI Lecture 1 Topics The concept of spin Precession of magnetic spin Relaxation Bloch Equation 1 Spin Intrinsic angular momentum of
More informationMetropolis Monte Carlo simulation of the Ising Model
Metropolis Monte Carlo simulation of the Ising Model Krishna Shrinivas (CH10B026) Swaroop Ramaswamy (CH10B068) May 10, 2013 Modelling and Simulation of Particulate Processes (CH5012) Introduction The Ising
More informationMagnetic Resonance Imaging (MRI)
Magnetic Resonance Imaging Introduction The Components The Technology (MRI) Physics behind MR Most slides taken from http:// www.slideworld.org/ viewslides.aspx/magnetic ResonanceImaging %28MRI%29MRImaging
More informationGeneral Physics (PHYS )
General Physics (PHYS ) Chapter 22 Magnetism Magnetic Force Exerted on a current Magnetic Torque Electric Currents, magnetic Fields, and Ampere s Law Current Loops and Solenoids Magnetism in Matter GOT
More informationChapter 21 dblock metal chemistry: coordination complexes
Chapter 21 dblock metal chemistry: coordination complexes Bonding: valence bond, crystal field theory, MO Spectrochemical series Crystal field stabilization energy (CFSE) Electronic Spectra Magnetic Properties
More informationPhysical Background Of Nuclear Magnetic Resonance Spectroscopy
Physical Background Of Nuclear Magnetic Resonance Spectroscopy Michael McClellan Spring 2009 Department of Physics and Physical Oceanography University of North Carolina Wilmington What is Spectroscopy?
More informationMagnetic Resonance Spectroscopy EPR and NMR
Magnetic Resonance Spectroscopy EPR and NMR A brief review of the relevant bits of quantum mechanics 1. Electrons have spin,  rotation of the charge about its axis generates a magnetic field at each electron.
More informationCorrelations between spin accumulation and degree of timeinverse breaking for electron gas in solid
Correlations between spin accumulation and degree of timeinverse breaking for electron gas in solid V.Zayets * Spintronic Research Center, National Institute of Advanced Industrial Science and Technology
More informationWarsaw University of Technology Electrical Department. Laboratory of Materials Technology KWNiAE
Warsaw University of Technology Electrical Department Laboratory of Materials Technology KWNiAE Practice 6 Analysis of Ferromagnetic Materials 1. Introduction In each atom of every known material there
More informationReport submitted to Prof. P. Shipman for Math 540, Fall 2009
Dynamics at the Horsetooth Volume 1, 009. ThreeWave Interactions of Spin Waves Aaron Hagerstrom Department of Physics Colorado State University aaronhag@rams.colostate.edu Report submitted to Prof. P.
More informationPhysics 1308 Exam 2 Summer 2015
Physics 1308 Exam 2 Summer 2015 E201 2. The direction of the magnetic field in a certain region of space is determined by firing a test charge into the region with its velocity in various directions in
More informationCrystal Field Theory
Crystal Field Theory It is not a bonding theory Method of explaining some physical properties that occur in transition metal complexes. Involves a simple electrostatic argument which can yield reasonable
More informationRelativistic corrections of energy terms
Lectures 23 Hydrogen atom. Relativistic corrections of energy terms: relativistic mass correction, Darwin term, and spinorbit term. Fine structure. Lamb shift. Hyperfine structure. Energy levels of the
More informationWith that first concept in mind, it is seen that a spinning nucleus creates a magnetic field, like a bar magnet
NMR SPECTROSCOPY This section will discuss the basics of NMR (nuclear magnetic resonance) spectroscopy. Most of the section will discuss mainly 1H or proton spectroscopy but the most popular nuclei in
More informationThermal and Statistical Physics Department Exam Last updated November 4, L π
Thermal and Statistical Physics Department Exam Last updated November 4, 013 1. a. Define the chemical potential µ. Show that two systems are in diffusive equilibrium if µ 1 =µ. You may start with F =
More informationcharges q r p = q 2mc 2mc L (1.4) ptles µ e = g e
APAS 5110. Atomic and Molecular Processes. Fall 2013. 1. Magnetic Moment Classically, the magnetic moment µ of a system of charges q at positions r moving with velocities v is µ = 1 qr v. (1.1) 2c charges
More informationChapter 8 Magnetic Resonance
Chapter 8 Magnetic Resonance 9.1 Electron paramagnetic resonance 9.2 Ferromagnetic resonance 9.3 Nuclear magnetic resonance 9.4 Other resonance methods TCD March 2007 1 A resonance experiment involves
More informationClass XII Chapter 4 Moving Charges And Magnetism Physics
Class XII Chapter 4 Moving Charges And Magnetism Physics Question 4.1: A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic
More informationThe experiment consists of studying the deflection of a beam of neutral ground state paramagnetic atoms (silver) in inhomogeneous magnetic field:
SPIN 1/2 PARTICLE SternGerlach experiment The experiment consists of studying the deflection of a beam of neutral ground state paramagnetic atoms (silver) in inhomogeneous magnetic field: A silver atom
More informationLecture Outlines Chapter 22. Physics, 3 rd Edition James S. Walker
Lecture Outlines Chapter 22 Physics, 3 rd Edition James S. Walker 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in
More informationThe Electronic Structure of Atoms
The Electronic Structure of Atoms Classical Hydrogenlike atoms: Atomic Scale: 1010 m or 1 Å +  Proton mass : Electron mass 1836 : 1 Problems with classical interpretation:  Should not be stable (electron
More informationPHYS4210 Electromagnetic Theory Quiz 1 Feb 2010
PHYS4210 Electromagnetic Theory Quiz 1 Feb 2010 1. An electric dipole is formed from two charges ±q separated by a distance b. For large distances r b from the dipole, the electric potential falls like
More 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 P361 Before Starting All of your grades should now be posted
More informationUses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and Deuterides. Mark S. Conradi
Uses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and Deuterides Mark S. Conradi Washington University Department of Physics St. Louis, MO 631304899 USA msc@physics.wustl.edu 1 Uses of Nuclear
More informationFinal Exam Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall Duration: 2h 30m
Final Exam Tuesday, May 8, 2012 Starting at 8:30 a.m., Hoyt Hall.  Duration: 2h 30m Chapter 39 Quantum Mechanics of Atoms Units of Chapter 39 391 QuantumMechanical View of Atoms 392
More informationMagnetic Torque Physics 2150 Experiment No. 11 University of Colorado
Experiment 11 1 Introduction Magnetic Torque Physics 2150 Experiment No. 11 University of Colorado In this experiment, you will study how a magnet moment interacts with a magnetic field. You will measure
More informationQuantum Mechanics & Atomic Structure (Chapter 11)
Quantum Mechanics & Atomic Structure (Chapter 11) Quantum mechanics: Microscopic theory of light & matter at molecular scale and smaller. Atoms and radiation (light) have both wavelike and particlelike
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 informationContents. Acknowledgments
MAGNETIC MATERIALS Fundamentals and Applications Second edition NICOLA A. SPALDIN University of California, Santa Barbara CAMBRIDGE UNIVERSITY PRESS Contents Acknowledgments page xiii I Basics 1 Review
More informationImportant Formulae & Basic concepts. Unit 3: CHAPTER 4  MAGNETIC EFFECTS OF CURRENT AND MAGNETISM CHAPTER 5 MAGNETISM AND MATTER
Iportant Forulae & Basic concepts Unit 3: CHAPTER 4  MAGNETIC EFFECTS OF CURRENT AND MAGNETISM CHAPTER 5 MAGNETISM AND MATTER S. No. Forula Description 1. Magnetic field induction at a point due to current
More informationLecture 14. Magnetic Forces on Currents. Hall Effect. Magnetic Force on a Wire Segment. Torque on a CurrentCarrying Loop.
Lecture 14. Magnetic Forces on Currents. Outline: Hall Effect. Magnetic Force on a Wire Segment. Torque on a CurrentCarrying Loop. Lecture 13: Magnetic Forces on Moving Charges  we considered individual
More informationMagnetism. (Unit Review)
Physics Name: Date: Period: Magnetism (Unit Review) Coronal mass ejection Diamagnetic Differential rotation Electric motor Electromagnet Electromagnetic induction Faraday s Law of Induction Galvanometer
More informationProblem Set 2 Due Thursday, October 1, & & & & # % (b) Construct a representation using five d orbitals that sit on the origin as a basis:
Problem Set 2 Due Thursday, October 1, 29 Problems from Cotton: Chapter 4: 4.6, 4.7; Chapter 6: 6.2, 6.4, 6.5 Additional problems: (1) Consider the D 3h point group and use a coordinate system wherein
More informationElectron configuration: shows which orbitals are occupied in an atom, and how many electrons they contain
ch8blank Page 1 Chapter 8: Periodic properties of the elements Electron configuration: shows which orbitals are occupied in an atom, and how many electrons they contain Ground state: lowest energy, most
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 informationChapter 8: Magnetic and Electrical Properties
Chapter 8: Magnetic and Electrical Properties 1 In solids, properties of individual atoms can interact cooperatively to produce effects not found in fluids. Magnetic Susceptibility: magnetic field produces
More informationLecture 17. Magnetic Materials. Electromagnetic Induction. Faraday s Law
Lecture 17. Magnetic Materials. Electromagnetic Induction. Faraday s Law Outline: Magnetic Materials. Faraday s Law. Sign Convention: Lenz s Law The 3 d Maxwell s Equation (in combination with the 4 th
More informationSolutions to chapter 4 problems
Chapter 9 Solutions to chapter 4 problems Solution to Exercise 47 For example, the x component of the angular momentum is defined as ˆL x ŷˆp z ẑ ˆp y The position and momentum observables are Hermitian;
More informationMolecular Term Symbols
Molecular Term Symbols A molecular configuration is a specification of the occupied molecular orbitals in a molecule. For example, N : σ gσ uπ 4 uσ g A given configuration may have several different states
More informationLecture 22. Inductance. Magnetic Field Energy.
Lecture 22. Inductance. Magnetic Field Energy. Outline: Selfinduction and selfinductance. Inductance of a solenoid. The energy of a magnetic field. Alternative definition of inductance. Mutual Inductance.
More informationMagnetic Fields. or I in the filed. ! F = q! E. ! F = q! v! B. q! v. Charge q as source. Current I as source. Gauss s Law. Ampere s Law.
Magnetic Fields Charge q as source Gauss s Law Electric field E F = q E Faraday s Law AmpereMaxwell Law Current I as source Magnetic field B Ampere s Law F = q v B Force on q in the field Force on q v
More informationPhysics 511 Spring 2000
Physics 511 Spring 2000 Problem Set #8: Due Friday April 7, 2000 Read: Notes on Multipole Radiation, Jackson Third Ed. Chap. 6.36.4, 9.19.4, Low 4.14.6 Problem 1. Electromagnetic radiation in one dimension
More informationMagnetic Force. A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?
Magnetic Force A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire? (a) left (b) right (c) zero (d) into the page (e) out of the page B
More informationOverhauser Magnetometers For Measurement of the Earth s Magnetic Field
Overhauser Magnetometers For Measurement of the Earth s Magnetic Field By: Dr. Ivan Hrvoic GEM Systems Inc. (Magnetic field Workshop on Magnetic Observatory Instrumentation Espoo, Finland. 1989) TABLE
More information1 Fundamental Constants, Elements, Units
1 Fundamental Constants, Elements, Units 1.1 Fundamental Physical Constants Table 1.1. Fundamental Physical Constants Electron mass m e = 9.10939 10 28 g Proton mass m p = 1.67262 10 24 g Atomic unit of
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 informationChapter 31. Faraday s Law
Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field dφ B ( I I ) E d s = µ o + d = µ o I+ µ oεo ds E B 2 Induction A loop of wire is connected to a sensitive
More 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. BiotSavart law 4. Magnetic force between currents 5. Applications of BiotSavart law 6. Ampere s law in differential form 7. Magnetic
More informationExam 2 Solutions. ε 3. ε 1. Problem 1
Exam 2 Solutions Problem 1 In the circuit shown, R1=100 Ω, R2=25 Ω, and the ideal batteries have EMFs of ε1 = 6.0 V, ε2 = 3.0 V, and ε3 = 1.5 V. What is the magnitude of the current flowing through resistor
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 P361 efore Starting All of your grades should now be posted
More informationThe magnetic properties of solids
CHAPTER W The magnetic properties of solids Explanation This chapter is a supplement to the book: Understanding the properties of matter by Michael de Podesta. Please note: The copyright of this chapter
More informationPHY132 Lecture 13 02/24/2010. Lecture 13 1
Classical Physics II PHY132 Lecture 13 Magnetism II: Magnetic torque Lecture 13 1 Magnetic Force MAGNETISM is yet another force that has been known since a very long time. Its name stems from the mineral
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? BiotSavart Law SetUp The magnetic field is
More informationThe Third Law of Thermodynamics
4 The Third Law of Thermodynamics 4.1. Entropy and Probability An isolated system changes spontaneously until it reaches a state of equilibrium, unless some external constraint exists to prevent this change.
More informationUnit 12B: Ampere's Law. Not Assigned. Ampere's Law
Unit 12B: Ampere's Law Ampere's Law 1 A 0.200A current is charging a capacitor that has circular plates 10.0 cm in radius. The plate separation is 4.00 mm. (a) What is the time rate of increase of electric
More informationProblem Set 2 Due Tuesday, September 27, ; p : 0. (b) Construct a representation using five d orbitals that sit on the origin as a basis: 1
Problem Set 2 Due Tuesday, September 27, 211 Problems from Carter: Chapter 2: 2ad,g,h,j 2.6, 2.9; Chapter 3: 1ad,f,g 3.3, 3.6, 3.7 Additional problems: (1) Consider the D 4 point group and use a coordinate
More informationLectures in Paleomagnetism, 2005 by Lisa Tauxe. Citation:
Lectures in Paleomagnetism, 2005 by Lisa Tauxe Citation: http://earthref.org/magic/books/tauxe/2005/ May 30, 2005 Tauxe, 2005 00 Lectures in Paleomagnetism Chapter 1 The Physics of Magnetism Suggested
More informationIntroduction to Magnetism and Magnetic Materials
Introduction to Magnetism and Magnetic Materials Second edition David Jiles Ames Laboratory, US Department of Energy Department of Materials Science and Engineering and Department of Electrical and Computer
More informationSpin Interactions. Giuseppe Pileio 24/10/2006
Spin Interactions Giuseppe Pileio 24/10/2006 Magnetic moment µ = " I ˆ µ = " h I(I +1) " = g# h Spin interactions overview Zeeman Interaction Zeeman interaction Interaction with the static magnetic field
More informationNuclear Magnetic Resonance
Nuclear Magnetic Resonance PRINCIPLES OF NMR SPECTROSCOPY Contents Principles of nuclear magnetic resonance The nmr spectrometer Basic principles in nmr application NMR tools used to obtain information
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 informationLecture 11: Polarized Light. Fundamentals of Polarized Light. Descriptions of Polarized Light. Scattering Polarization. Zeeman Effect.
Lecture 11: Polarized Light Outline 1 Fundamentals of Polarized Light 2 Descriptions of Polarized Light 3 Scattering Polarization 4 Zeeman Effect 5 Hanle Effect Fundamentals of Polarized Light Electromagnetic
More informationChapter 23. Transition Metals and Coordination Chemistry
Chapter 23 Transition Metals and Coordination Chemistry The Transition Metals: Exact Definition Transition metal: An element whose atom has an incomplete d subshell or which can give rise to cations with
More informationBasic MRI physics and Functional MRI
Basic MRI physics and Functional MRI Gregory R. Lee, Ph.D Assistant Professor, Department of Radiology June 24, 2013 Pediatric Neuroimaging Research Consortium Objectives Neuroimaging Overview MR Physics
More informationATOMIC STRUCTURE, ELECTRONS, AND PERIODICITY
ATOMIC STRUCTURE, ELECTRONS, AND PERIODICITY All matter is made of atoms. There are a limited number of types of atoms; these are the elements. (EU 1.A) Development of Atomic Theory Atoms are so small
More informationChapter 6. Quantum Theory of the Hydrogen Atom
Chapter 6 Quantum Theory of the Hydrogen Atom 1 6.1 Schrodinger s Equation for the Hydrogen Atom Symmetry suggests spherical polar coordinates Fig. 6.1 (a) Spherical polar coordinates. (b) A line of constant
More information