§5.1: Magnetic fields
Christopher Crawford
PHY 311
2014-03-28
Outline
•
•
•
•
•
Introduction to magnetism
History of magnetism
Magnetic fields
Review: current
Lorentz force
2
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
3
Equations of Electrodynamics
4
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 1200 AD 1259 AD 1600 AD 1742 AD 1820 AD 1820 AD 1820 AD
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
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
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
7
First connection to currents:
• from Wittaker, “A history of the theories of Aether and Electricity”
8
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
9
Hans Christian Ørsted:
• from Wittaker, “A history of the theories of Aether and Electricity”
10
Electrodynamics
• Andre Marie Ampere shows that parallel currents attract
and antiparallel currents repel
• The magnetic force is the basis for electromagnetic units
11
Current elements
• Analogous to charge elements – different dimensions
• Relations between charge / current and different dimensions
– analogy: multi-lane highway
– current flux
12
Continuity equation
• Local conservation of charge
• Current I is a flux; current density J = flux density
• 4-vector current
13
Lorentz force
14