Physics 712 – Electricity and Magnetism Everyone Pick Up: Syllabus Two homework passes Materials Classical Electrodynamics by John David Jackson Calculator Pencils or pens, paper Symbolic manipulation Eric Carlson “Eric” “Professor Carlson” Olin 306 Office Hours always 758-4994 (o) 407-6528 (c) ecarlson@wfu.edu http://users.wfu.edu/ecarlson/eandm/index.html 1/13

Dr. Carlson’s Approximate Schedule Monday Tuesday Wednesday Thursday Friday 9:00 research research 10:00 PHY 712 office hour PHY 712 office hour PHY 712 11:00 PHY 742 office hour PHY 742 office hour PHY 742 12:00 PHY 109 office hour PHY 109 office hour PHY 109 1:00 2:00 research research research research 3:00 Collins Hall 4:00 Free food colloquium Collins Hall 5:00 Lab Meeting I will try to be in my office Tues. Thurs. 10-12 When in doubt, call/email first

Classical Electrodynamics by J.D. Jackson, 3rd Edition Reading Assignments / The Text Classical Electrodynamics by J.D. Jackson, 3rd Edition I’m not writing my own textbook Contains useful information Reading assignments every day ASSIGNMENTS Day Read Homework Today none none Friday 1.1-1.4 0.1 Wednesday 1.5-1.8 1.1, 1.2

Homework http://users.wfu.edu/ecarlson/quantum Problems assigned as we go along About one problems due every day Homework is due at 10:00 on day it is due Late homework penalty 20% per day Two homework passes per semester Working with other student is allowed Seek my help when stuck You should understand anything you turn in ASSIGNMENTS Day Read Homework Today none none Friday 1.1-1.4 0.1 Wednesday 1.5-1.8 1.1, 1.2

Attendance and Tests Tests Attendance I do not grade on attendance Attendance is expected Class participation is expected I take attendance every day Tests Midterm will be from 10-12 on March 4 Final will be from 9-12 on April 29

Percentage Breakdown: Grades, Pandemic Plans Grade Assigned 94% A 77% C+ 90% A- 73% C 87% B+ 70% C- 83% B <70% F 80% B- Percentage Breakdown: Homework 50% Midterm 20% Final 30% Some curving possible Emergency contacts: Web page email Cell: 336-407-6528 Pandemic Plans If there is a catastrophic closing of the university, we will attempt to continue the class:

0A. Math Coordinate Systems We will generally work in three dimensions A general coordinate in 3d will be denoted x A general vector will be shown in bold face v We will often work in Cartesian coordinates Sometimes in spherical coordinates, related to Cartesian by Coordinate x is Sometimes in cylindrical coordinates, related to Cartesian by

Vector Identities Vectors can be combined using dot products to make a scalar Vectors can be combined using cross-products to make a vector We often abbreviate Some vector identities: Symmetry/antisymmetry: Triple scalar product: Double cross-product: These and many others in Jackson front cover

Derivatives in 3D The vector derivative  can be used for several types of derivatives: Gradient turns a scalar function into a vector function Divergence turns a vector function into a scalar function Curl turns a vector function into a vector function There is also the Laplacian, a second derivative that can act on scalar or vector functions Each of these has more complicated forms in non-Cartesian coordinates See QM lecture notes or inside back cover of Jackson

Derivatives Product rule The product rule for derivatives: Numerous 3D equivalents for products Gradient of product of scalars Divergence of scalar times vector Curl of scalar times vector Divergence of a cross product Each of these and many more in Jackson, front cover

Integrals in 3D 3d integrals of vector scalar functions will be common You should know how to handle these in any coordinate system Cartesian: Spherical: Cylindrical:

Fundamental Theorem of Calculus in 3D Fundamental theorem of calculus says: In general, in 3d, this theorem lets you do one integral whenever you have an integral in 3d: Line integral: Stokes’ Theorem: Divergence Theorem: Another theorem: And another theorem: All these and more can be found on inside front cover of Jackson

Sample Problem 0.1 Work in spherical coordinates For x  0, take divergence Tricky at x = 0 because everything is infinite there! Integrate over a sphere of radius R using the divergence theorem: Since the integral is zero except at the origin, we must have You can generalize this where x is replaced by the difference from an arbitrarily chosen origin x': Consider the vector function x/|x|3 . (a) Find the divergence for x  0. (b) By integrating over a sphere around the origin, show that the divergence does not vanish there. R

0B. Units Units is one of the most messed-up topics in electricity and magnetism We will use SI units throughout Fundamental units: From these are derived lots of non fundamental units: Equations of E and M sometimes depends on choice of units! Distance meter m Time second s Mass kilogram kg Charge coulomb C Frequency hertz Hz s–1 Force newton N kgm/s2 Energy joule J Nm Power watt W J/s Current amp A C/s Potential volt V J/C Resistance ohm  V/A Magnetic induction tesla T kg/C/s Magnetic flux weber Wb Tm2 Inductance Henry H Vs/A