Christopher Crawford 2015-01-14 PHY 417G: Introduction Christopher Crawford 2015-01-14

Outline Announcements Syllabus; schedule: HW due, recitations Grades – distribution, Feedback – discussion REU opportunities – ex: accelerator physics Introduction Ridiculously brief history of E&M Math review: linear + differential spaces, fund. theorems E&M review/overview: mathematical structure

Announcements Syllabus: pa.uky.edu  about  courses  417 HW schedule: recitations?, due day? Office hours? Exams? Grades: Final Grade Final Exam Feedback Your participation in class changes everything! REU positions http://www.anl.gov/education/undergraduates/internship-opportunities/lee-teng-undergraduate-fellowship-accelerator

History of magnetism The magnetic force was known in antiquity Magnetism more predominant in nature but more difficult to quantify: Permanent magnets (magnetization), not electric currents No magnetic (point) charge (monopole) –> dipole effect (N,S poles) 1-d currents instead of 0-d charges –> can’t split a wire! Static electricity produced in the lab long before steady currents Timeline (from “A Ridiculous Brief History of Electricity and Magnetism”) 600 BC Thales of Miletus discovers lodestone’s attraction to iron 1200 AD Chinese use lodestone compass for navigation 1259 AD Petrus Peregrinus (Italy) discovers the same thing 1600 AD William Gilbert discovers that the Earth is a giant magnet 1742 AD Thomas LeSeur shows inverse cube law for magnets 1820 AD Hans Christian Ørsted discovers that current twists magnets Andre Marie Ampere shows that parallel currents attract/repel Jean-Baptiste Biot & Felix Savart show inverse square law

Unification of 4 Fundamental Forces

Classical Fields action at a distance vs. locality field ”mediates “carries force extends to quantum field theories field is everywhere always E (x, t) differentiable, integrable field lines, equipotentials powerful techniques for solving complex problems

Magnetic fields In magnetism it is more natural to start with the concept of “Magnetic field” than the actual force law! (dipole) Compass aligns with B-field Iron filings line up along magnetic field lines Magnetic field lines look like an electric dipole (in fact the magnetic dipole was discovered first!)

Difference between E, B dipoles Same as the differences between Flux and Flow! Charge = sources of flux Conservative flow [potential] Example: Amber (electric) Rub to charge 2 charges (+/–) “monopole fluids” Exerts force on charges Continuous field lines [flux] Rotational (source of flow?) Example: Lodestone (magnet) Always charged 2 poles (N/S) “inseparable dipole” Exerts torque on other magnets

Formulations of E & M Electricity Magnetism Note the interchange of flux and flow: twisted symmetry!

Magnetic scalar potential Electrostatics – Coulomb’s law Magnetostatics – Biot-Savart law Geometrical Gauss -> Ampere’s law U interpretation as boundary currents Statement in terms of boundary conditions Technique for calculating coils B.C.’s: Flux lines bounded by charge Flux lines continuous Flow sheets continuous (equipotentials) Flow sheets bounded by current

L/T separation of E&M fields

Equations of Electrodynamics

Polarization & Magnetization Chapter 4: electric materials –> Chapter 6: magnetic materials Polarization chain –> Magnetization mesh

3 Materials –> 3 Components Materials constants: permittivity, resistivity, permeability Electrical components: capacitor, resistor, inductor Each is a ratio of Flux / Flow !