Christopher Crawford PHY

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Christopher Crawford PHY 417 2015-02-13 §6.4 Magnetic Media Christopher Crawford PHY 417 2015-02-13

Outline Magnetic Materials B = μ0 (H+M) = μ0 (1+χm)H = μ0μr H = μH vs. electric: D = ε0 E + P = ε0 (1+χe )E = ε0εr E = εE Constitutive relation and Magnetic susceptibility Linear & nonlinear magnetic materials Maxwell equations and Boundary conditions Boundary value problem #1 Sphere of constant magnetization M use magnetic pole density σM Boundary value problem #2 use bound current density Kb Boundary value problem #3 Permeable sphere in a constant background field H0 Use permeability μ

Geometry of fields Polarization chains vs. magnetization meshs

Static Macroscopic Maxwell Equations Electric Magnetic Constitutive equations Susceptibilities: permittivity and permeability

Magnetic media

Magnetic media

Boundary Conditions Electric Magnetic Two redundant sources – Three redundant sources!

Boundary value problem #1

Boundary value problem #2

Boundary value problem #3