Download Fundamental nuclear symmetries meet classical electrodynamic

§5.1: Magnetic Field
Christopher Crawford
PHY 417
2015-01-16
Outline
• Magnetic field and torque
William Gilbert – field lines of permanent magnets
Hans Christian Ørsted – magnetic field of a current
• Magnetostatics
André-Marie Ampère – force on two straight wires
Current element – continuity equation
2
Static force laws
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
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
Early magnetism
https://www.tcd.ie/Physics/Magnetism/Guide/compass.php
•Wu Ching Tsung Yao (1040)
– First mention of the magnetic compass
•Petrus Perigrinus (1269)
– “Epostolia de Magnete” – rediscovered it
•William Gilbert (1600)
– “De Magnete” – the earth is a magnet
•René Descartes
– effluvia of "threaded parts”
5
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!)
6
Iron Filings
7
Iron Filings
8
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
9
First connection to currents:
• from Wittaker, “A history of the theories of Aether and Electricity”
10
The current connection
• There is no magnetic monopole – N/S cannot be separated
• The source of all magnetism is electric current
– A dipole is just a current loop
• Hans Christian Ørsted
– Current produces B-field
– Quantified by Biot & Savart
11
Hans Christian Ørsted:
• from Wittaker, “A history of the theories of Aether and Electricity”
12
Electrodynamics
• André-Marie Ampère showed that parallel currents attract
and antiparallel currents repel
• The magnetic force is the basis for electromagnetic units
13
Ampère’s generalization
• Experimental laws:
• Force formula
• Problem
– The force between two current elements does NOT
point along the line from the one to the other!
14
HEAVISIDE
MAXWELL
Peer criticism
15
Current elements
• Analogous to charge elements – different dimensions
• Relations between charge / current and different dimensions
– analogy: multi-lane highway
– current flux
16
Continuity equation
• Local conservation of charge
• Current I is a flux; current density J = flux density
• 4-vector current
17