Transcript Fundamental nuclear symmetries meet classical

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
2
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/internshipopportunities/lee-teng-undergraduate-fellowship-accelerator
3
History of magnetism
• The magnetic force was known in antiquity
– Magnetism more predominant in nature but more difficult to quantify:
1.
2.
3.
4.
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
4
Unification of 4 Fundamental Forces
5
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
6
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!)
7
Difference between E, B dipoles
• Same as the differences between Flux and Flow!
• Charge = sources of flux
• Continuous field lines [flux]
• Conservative flow [potential] • Rotational (source of flow?)
• Example: Amber (electric)
• Example: Lodestone (magnet)
– Rub to charge
– 2 charges (+/–) “monopole fluids”
– Exerts force on charges
– Always charged
– 2 poles (N/S) “inseparable dipole”
– Exerts torque on other magnets
8
Formulations of E & M
• Electricity
Magnetism
• Note the interchange of flux and flow: twisted symmetry!
9
Magnetic scalar potential
Electrostatics – Coulomb’s law
B.C.’s:
Magnetostatics – Biot-Savart law
Flux lines bounded by charge
Flow sheets continuous (equipotentials)
Flux lines continuous
Flow sheets bounded by current
10
L/T separation of E&M fields
11
Equations of Electrodynamics
12
Polarization & Magnetization
• Chapter 4: electric materials –> Chapter 6: magnetic materials
• Polarization chain
–> Magnetization mesh
13
3 Materials –> 3 Components
• Materials constants: permittivity, resistivity, permeability
• Electrical components: capacitor, resistor, inductor
• Each is a ratio of Flux / Flow !
14