Northeastern Illinois University
Electricity & Magnetsim I
Vector Calculus I
Greg Anderson Department of Physics & Astronomy Northeastern Illinois University
Spring 2010
c 2004-2010 G. Anderson
Electricity & Magnetism I
slide 1 / 31
Northeastern Illinois
2
JACOB LEWIS BOURJAILY
We should note that this more-or-less agrees with the expressions for the potential worked out in the text for similar circumstances. In particular, Jackson's equation (3.36) describes a similar problem, where = - V /2 on the inner
EP 364 SOLID STATE PHYSICS
Course Coordinator Prof. Dr. Beire Gnl
INTRODUCTION
AIM OF SOLID STATE PHYSICS WHAT IS SOLID STATE PHYSICS AND WHY DO IT? CONTENT REFERENCES
EP364 SOLID STATE PHYSICS INTRODUCTION
Aim of Solid State Physics
Solid state physi
CHAPTER 2 INTERATOMIC FORCES
What kind of force holds the atoms together in a solid?
Interatomic Binding
All of the mechanisms which cause bonding between the atoms derive from electrostatic interaction between nuclei and electrons.
The differing strength
CHAPTER 2 INTERATOMIC FORCES
What kind of force holds the atoms together in a solid?
Interatomic Binding
All of the mechanisms which cause bonding between the atoms derive from electrostatic interaction between nuclei and electrons. The differing strength
CHAPTER 3 XRAY DIFFRACTION IN CRYSTAL
I. II. III. IV. V. VI.
Bertha Rntgen's Hand 8 Nov, 1895
1
VII.
X-Ray Diffraction Diffraction of Waves by Crystals X-Ray Diffraction Bragg Equation X-Ray Methods Neutron & Electron Diffraction
XRAY
X-rays were discover
SOUND WAVES LATTICE VIBRATIONS OF 1D CRYSTALS
chain of identical atoms chain of two types of atoms
LATTICE VIBRATIONS OF 3D CRYSTALS PHONONS HEAT CAPACITY FROM LATTICE VIBRATIONS ANHARMONIC EFFECTS THERMAL CONDUCTION BY PHONONS
Crystal Dynamics
Con
CHAPTER 5 FREE ELECTRON THEORY
Free Electron Theory
Many solids conduct electricity. There are electrons that are not bound to atoms but are able to move through the whole crystal. Conducting solids fall into two main classes; metals and semiconductor
Chapter 1: Crystal Structure
The Nobel Booby Prize!
See the Ig Nobel Prize discussed at: http:/improbable.com/ig/
Phases of Matter
Matter Gases
Liquids & Liquid Crystals
Solids
Condensed Matter actually includes both of these. Well focus on Solids!
Gases
CRYSTALLATTICE
What is crystal (space) lattice? In crystallography, only the geometrical properties of the crystal are of interest, therefore one replaces each atom by a geometrical point located at the equilibrium position of that atom.
Platinum
Platinum
Examples
We can move vector to the origin.
X =-1 , Y = 1 , Z = -1/6 [-1 1 -1/6] [6 6 1]
Crystal Structure 1
CrystalPlanes
Within a crystal lattice it is possible to identify sets of equally spaced parallel planes. These are called lattice planes. In the
<?xml version="1.0" encoding="UTF-8"?> <Error><Code>NoSuchKey</Code><Message>The specified key does not exist.</Message><Key>304c395668ac1621c245ad35bb1561792cb4b648.ppt</Key><RequestId>2 95B1BEBCB1FFF18</RequestId><HostId>w4iDHqwEJL/hdhyd3eCl9f787i45La9C
bBody Centered Cubic (BCC)
BCC has two lattice points so BCC is a non-primitive cell. BCC has eight nearest neighbors. Each atom is in contact with its neighbors only along the bodydiagonal directions. Many metals (Fe,Li,Na.etc), including the alkalis and
cFaceCenteredCubic(FCC)
There are atoms at the corners of the unit cell and at the center of each face. Face centered cubic has 4 atoms so its non primitive cell. Many of common metals (Cu,Ni,Pb.etc) crystallize in FCC structure.
Crystal Structure
1
Ato
Physics 505 Homework Assignment #4 Solutions
Fall 2005
Textbook problems: Ch. 3: 3.4, 3.6, 3.9, 3.10
3.4 The surface of a hollow conducting sphere of inner radius a is divided into an even number of equal segments by a set of planes; their common line of
u t u T 2 xwt u vw vu ctt r W s w u W 2t r w u r u 2 t W w u ` u vT ! xw u 2 R V u fW V UTR r ` ! &xgAIy a u t t R R u vT su V W u V u fW V UTR r f u T u i V u fW V UTR u u W 2 xu 03 % 8 7E %' 8 7 8 ( 7 70 5 ( w % u j6) u I5I8&gB!F3)ag(!3( # 2F096dg86X66
Northeastern Illinois University
Electricity & Magnetsim I
Vector Calculus II
Greg Anderson Department of Physics & Astronomy Northeastern Illinois University
Spring 2010
c 2004-2009 G. Anderson
Electricity & Magnetism I
slide 1 / 34
Northeastern Illinoi
Northeastern Illinois University
Electricity & Magnetsim I
Vector Calculus III
Greg Anderson Department of Physics & Astronomy Northeastern Illinois University
Spring 2010
c 2004-2009 G. Anderson
Electricity & Magnetism I
slide 1 / 34
Northeastern Illino
Chapter 1
Introductory material
Last revised 9 October 2008 This chapter gives a quick review of some of those parts of the prerequisite courses (Calculus I and II and Geometry I) which we will actually use, adding some extra material. Those parts which a
Chapter 7
Fourier series
Syllabus section: 6. Fourier series: full, half and arbitrary range series. Parseval's Theorem. Fourier series can be obtained for any function defined on a finite range, as in the S-L section above. In practice they provide a way
Chapter 4
Index Notation and the Summation Convention
Syllabus covered: 3. Index notation and the Summation Convention; summation over repeated indices; Kronecker delta and i jk ; formula for i jk klm . We now introduce a very useful notation. In particul
Lecture Notes for
MAS204: CALCULUS III
M.A.H. MacCallum These notes are based on independent previous versions by M.J. Thompson, with figures by C.D. Murray, and by P. Saha.
School of Mathematical Sciences, Queen Mary, University of London September-Decem
Chapter 5
Orthogonal Curvilinear Coordinates
Syllabus section: 4. Orthogonal curvilinear coordinates; length of line element; grad, div and curl in curvilinear coordinates; spherical and cylindrical polar coordinates as examples. So far we have only used
Chapter 6
Series solutions of ODEs and special functions
Syllabus section: 5. Series solution of ODEs. Introduction to special functions, e.g., Legendre, Bessel, and Hermite functions; orthogonality of special functions.
6.1 Context
[This section is not i
Chapter 2
Vector differentiation and the vector differential operator
Syllabus topics covered: 1. Vector fields 2. Grad, div and curl operators in Cartesian coordinates. Grad, div, and curl of products etc. Here we cover differentiation of vectors. This
Chapter 3
Vector integrals and integral theorems
Syllabus covered: 1. Line, surface and volume integrals. 2. Vector and scalar forms of Divergence and Stokes's theorems. Conservative fields: equivalence to curl-free and existence of scalar potential. Gree
Assignment 1 Solution
Wednesday, October 01, 2008 9:11 PM
3.21
Every point on the ring is the same distance from a point on the z-axis, so the potential at z is
Electric field along z-axis: By symmetry, it's only in the zdirection
3.22 By spherical symmet
Sodium Chlor ide Str uctur e
This structure can be considered as a facecentered-cubic Bravais lattice with a basis consisting of a sodium ion at 0 and a chlorine ion at the center of the conventional cell,
a / 2( x +y +z )
LiF,NaBr,KCl,LiI,etc The lat