1. Christopher Crawford PHY 416 2015-02-09
§6.1–2 Magnetization
Christopher Crawford
PHY 416

2. Outline Magnetic Polarizability m=I a =βB compare: p=q d =αE
Diamagnetism β compare: α
Paramagnetism β compare: α
Ferromagnetism
Magnetization Density M=dm/dτ compare: P=dp/dτ WORKING GROUPS:
Magnetization sheets flow compare: ?
Magnetization solenoids flux compare: ΦP
Magnetization currents Jb, Kb compare: ρb, σb

3. Diamagnetism Induced electric polarizability αe of all molecules
Bound charge is ‘stretched’ in the direction of the electric field
Diamagnetism
Gyromagnetic ratio: m vs L
Magnetization opposite direction of B field!
Compare direction of Eb, Bb
2000 Ig Nobel Prize

4. Paramagnetism Recall PHY416 HW9 #2 “the Langevin formula”
Electric polarizability αe of permanent dipoles
Thermal fluctuations prevent dipoles from perfect alignment
Paramagnetism
Exhibited in all atoms, stronger than diamagnetism
Often cancelled out by Pauli exclusion principle (paired electrons)
Ferromagnetism
B-field is strengthened as dipoles align with the field
For strong magnetic dipoles below the Curie temperature, magnetic dipoles can self-align into a ‘magnetic crystal’
Domains of uniformly strongly magnetized dipoles create up to 106 amplification of the magnetic intensity H

5. Review: Polarization chain
Dipole density P = dp/dτ = dq/da = σ (l=1)
Versus charge density ρ = dq/dτ (l=0)
Units: C/m2
Dipole chain – polarization flux dΦP = P  da
Gauss-type law
Units: C
Back-field -ε0Eb
Charge screening
Geometry-dependent
Example: sphere
Displacement flux D
Between free change
Continuity between E-flux and P-chains

6. Comparison and contrast
Electric flux
Polarization chains

7. Field due to a polarization distribution
Differences for Magnetization
Vector potential
Generalized volume-boundary theorems: Div, Curl, & Grad:

8. Working groups Develop the geometry of magnetization meshes
Compare and contrast to: electric polarization chains
Comparison and contrast magnetization current Jf vs Jb
Relation to magnetic/magnetization surfaces of H and M
Compare and contrast to: electric polarization ρf vs ρb
Derivation of bound potential
Compare and contrast to: electric bound potential
Reconcile results with Working Group #1