20.1 - Chapter 20: Magnetic Properties ISSUES TO ADDRESS.....

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Unformatted text preview: Chapter 20: Magnetic Properties ISSUES TO ADDRESS.. • How do we characterize magnetic properties? • What are the atomic reasons for magnetism? • How are magnetic materials classified? • Materials design for magnetic storage • (What is the importance of superconducting magnets?) Chapter 20 - 1 ANNOUNCEMENTS Download: Web Chapters 20 and 21 from BbVista Reading: Chapter 20, All Sections except 20.8 Week 9 Recitations: Quiz on Chapter 18 (Electrical Properties) Review Midterm 2: Same procedure & policy re. Q’s, addition errors, mis-grades, etc…return to RA… Problems: 20.1, 20.4, 20.5, 20.7, 20.17 and 20.21 No Quiz on these in Recitation - included in Final Exam Midterm 2: Average etc.: Ave.: 66.85 (68.47 in 2009) HI: 98 (99) LO: 25 (16) Chapter 20 - 2 ANNOUNCEMENTS Final Exam: Friday, June 11, 1:00-3:00 pm, Main Auditorium Accommodations: LeBow 348; 1:00-4:00 (1.5X); 1:00-5:00 (2X) Coverage: Chapters 17, 18, 20, 21 + some topics from previous chapters/earlier material… Style: Like 2 Midterms…1 x multipart, short answer/circle the answer type question + 5 recitation problem style questions, including one 15 point (~9%) bonus Q Keys to Success: Read the textbook & posted lecture notes Read your own lecture notes Practice solving problems…recitation, example, other Take advantage of RA and/or TA office hours Chapter 20 - 3 ANNOUNCEMENTS Course Evaluations: Open Tuesday, 5/26/10 Close, Friday, 6/19/10 Please complete an evaluation of the course, the various instructors…maybe after the final exam etc. o Your feedback provides us with useful information which we use to make changes in the future Chapter 20 - 4 Background Origins of Magnetic Forces Moving electrically charged particles… Think in terms of magnetic fields… Current loop or bar magnet w. lines of force Magnetic dipoles in magnetic materials…akin to electric dipoles (Van der Waals, polarization) Compare N-S vs. + Magnetic dipoles affected by magnetic fields in way that electric dipoles affected by electric fields Field exerts force (torque) which tends to align dipoles with applied field Chapter 20 - 5 Magnetic Field Lines Current Loop Bar Magnet Chapter 20 - 6 Applied Magnetic Field (Field Vector) • Created by current (I) flowing through a coil: Externally applied magnetic field H current I N = total number of turns L = length of solenoid (not wire) H also called magnetic field strength • Relation for the applied magnetic field, H: # Turns NI H= L Applied magnetic field units = (Ampere-turns/m) Current (A) Coil length (m) Chapter 20 - 7 Magnetic Flux Density (Field Vector) Flux Density or Induction, B Magnitude of internal field strength within material subjected to H-field Units: Tesla B = μH μ = permeability…property of medium through which Hfield passes and B-field is measured In vacuum: B0 = μ0H μ0 = permeability of vacuum (4 x 10-7 H/m) μr = μ μ0 μr = relative permeability (unitless) Chapter 20 - 8 Magnetic Permeability, Magnetization… • μr = measure of degree to which material can be magnetized, or ease that B-field can be induced in presence of external H-field • Magnetization of solid, M Defined by B = μ0H + μ0M In presence of H-field, magnetic moments within material align with field and reinforce it by virtue of their magnetic fields (μ0M) Magnitude of M proportional to applied H-field: • M = mH • m = magnetic susceptibility (also unitless) It can be easily shown that: • m = μr - 1 Chapter 20 - 9 B = μoH + μo m H = 4 x 10-7 (1.257 x 10-6) H/m o m = magnetic susceptibility; dimensionless Chapter 20 - 10 Measuring Magnetic Props. Chapter 20 - 11 Chapter 20 - 12 Response to a Magnetic Field • Magnetic induction B results in a material subjected to H-field B = Magnetic Induction (Tesla) (within the material) B = μ o H + μ o mH B = 1+ m μ 0 H current I ( • Magnetic susceptibility, B m m (dimensionless) >0 vacuum < m H 0 ) indicates the material response relative to a vacuum m m =0 Chapter 20 - 13 Magnetic Moments • Macroscopic magnetic properties of materials: – consequence of magnetic moments associated with individual electrons – quantum mechanics simplified treatment Chapter 20 - 14 Magnetic Moments • Every electron has magnetic moments from 2 sources: – orbital motion of e- around nucleus: • • • • e- = moving charge consider as small current loop current loop generates small magnetic field magnetic moment along axis of rotation – electron spin: • spin up or down (± 1/2) around an axis – consider each e- as small magnet with orbital and spin magnetic moments – Fundamental magnetic moment: • • • • Bohr magneton… μB = 9.27 x 10-24 A-m2 spin magnetic moment = ± μB orbital magnetic moment = ml μB where ml = magnetic quantum # Chapter 20 - 15 Magnetic Moments Indicates response of electrons to a magnetic field Net magnetic moment: sum of magnetic moments from all electrons orbital moments of some e- pairs will cancel each other same true for spin moments… • e.g. e- with spin up will cancel e- with spin down net magnetic moment = sum of magnetic moments of all e- (both orbital and spin), taking cancellation into account For atom with completely filled electron shells/subshells: • total cancellation of both orbital and spin moments • such materials cannot be permanently magnetized! • e.g. He, Ne, Ar, etc. • Three types of response... Chapter 20 - 16 In general, assume that each unpaired electron contributes one Bohr magneton, B, to total Also assume that the orbital magnetic moment is quenched, i.e. it is zero For a material with magnetization, M: B = μ0 ( H + M ) = μ0μr H Chapter 20 - 17 Unpaired Electrons! No unpaired electrons means no magnetism… You cannot have magnetism without unpaired electrons If the electrons are paired… no magnetism! If you want magnetism make sure there are unpaired electrons Chapter 20 - 18 3 Types of Magnetism B = (1+ m )μ oH Permeability of vacuum: (1.26 x 10-6 H/m) Magnetic Induction B (Tesla) (3) Ferromagnetic e.g. Ferrite ( ), Co, Ni, Gd Ferrimagnetic e.g. Fe3O4, NiFe2O4 ( m as large as 106!) (2) Paramagnetic ( m ~10-4) e.g., Al, Cr, Mo, Na, Ti, Zr Vacuum ( = 0) (1) Diamagnetic ( m ~ -10-5) e.g. Al2O3, Cu, Au, Si, Ag, Zn Applied Magnetic Field H (Ampere-turns/m) Chapter 20 - 19 Diamagnetism • Diamagnetism: opposing (1) Diamagnetic none very weak, non-permanent…persists only when ext. H-field applied induced by change in orbital motion of e- due to applied field induced magnetic moment v. small, in direction opposite to applied field… No Applied Applied Magnetic Field (H = 0) Magnetic Field (H) Adapted from Fig. 20.5(a), Callister 7e. μr <1 susceptibility = -ve, i.e. B-field induced is less than in vacuum found in all materials, but only observable when other types of magnetism absent no practical importance Chapter 20 - 20 ...
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