Calculated physical quantities in AC magnetics

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The following local and integral physical quantities are calculated in the process of harmonic magnetic field analysis.

Local quantities:

• Complex amplitude of vector magnetic potential A (flux function rA in axisymmetric case);
• Complex amplitude of voltage U applied to the conductor;
• Complex amplitude of total current density j_total = j_external + j_eddies,
  source current density j_external
  and eddy current density j_eddies = –iωσA;
• Complex vector of the magnetic flux density B = curl A
  Planar case: \[ B_x = \frac{\partial A}{\partial y}, \quad B_y = -\frac{\partial A}{\partial x} \]

  Axisymmetric case: \[ B_z = \frac{1}{r}\frac{\partial (rA)}{\partial r}, \quad B_r = -\frac{\partial A}{\partial z} \]

• Complex vector of magnetic field intensity \[ \mathbf H = μ^{-1} · \mathbf B \] where μ is the magnetic permeability tensor;
• Time average and peak Joule heat density \[ Q = σ^{-1}j^2 + k_hfB^2 + k_cf^2B^2 + k_e(f·B)^{1.5} ;\]
• Time average and peak magnetic field energy density \[ w = \frac{1}{2}\left (\mathbf B · \mathbf H \right ) ; \]
• Time average Poynting vector (local power flow) \[ \mathbf S = \mathbf E × \mathbf H ; \]
• Time average Lorentz force density vector \[ \mathbf F = \mathbf j × \mathbf B ; \]
• Magnetic permeability μ (its largest component in anisotropic media);
• Electric conductivity σ.

Integral quantities:

See section Integral quantities in AC magnetics.