Physics 712 – Electricity and Magnetism

1. Everyone Pick Up: • Syllabus • Two homework passes Materials • Classical Electrodynamics by John David Jackson • Calculator • Pencils or pens, paper • Symbolic manipulation Physics 712 – Electricity and Magnetism 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

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

3. 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 DayReadHomework Today none none Friday 1.1-1.4 0.1 Wednesday 1.5-1.8 1.1, 1.2

4. 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 DayReadHomework Today none none Friday 1.1-1.4 0.1 Wednesday 1.5-1.8 1.1, 1.2

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

6. 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:

7. 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 inspherical coordinates,related to Cartesian by • Coordinate x is • Sometimes incylindrical coordinates,related to Cartesian by • Coordinate x is

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

9. Derivatives in 3D • The vector derivative  can be used for several types of derivatives: • Gradient turns a scalar functioninto a vector function • Divergence turns a vectorfunction into a scalar function • Curl turns a vectorfunction into avector function • There is alsothe Laplacian, a secondderivative that can act onscalar or vector functions • Each of these has more complicated forms in non-Cartesian coordinates • See QM lecture notes or inside back cover of Jackson

10. 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

11. 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:

12. Fundamental Theorem of Calculus in 3D • Fundamental theorem of calculus says: • In general, in 3d, this theorem lets you doone 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

13. Sample Problem 0.1 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. • Work insphericalcoordinates • 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 thedifference from an arbitrarily chosen origin x': R

14. 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 ofnon fundamental units: • Equations of E and M sometimesdepends 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