Christopher Crawford PHY

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Presentation transcript:

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

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

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 http://www.ru.nl/publish/pages/682806/frog-ejp.pdf

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

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

Comparison and contrast Electric flux Polarization chains

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

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