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# ssp_22b - 7 Magnetic properties B = 0(H M(7.1 Magnetic...

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7-1 7 Magnetic properties Magnetic induction B = µ 0 ( H + M ) (7.1) (magnetic flux density) H : magnetic field density, M : magnetization, µ 0 = 4 π × 10 -7 Vs/Am: permeability of free space Vacuum: M = 0 In matter: = i i m V M 1 sum of magnetic moments / volume (7.2) Fig. 7.1 A loop current gives rise to a torque in a magnetic field given by IA × B . The quantity IA is defined as magnetic moment. Lorentz force on conduction loop torque T = I A × B = m × B (7.3) with magnetic moment: m = I A

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7-2 Potential energy of a dipole in a homogeneous magnetic field α α α α α α π α π cos sin ) ( 2 / 2 / = = = mB d mb Td E choise of zero point: E = 0 for m B E = -m B Force in inhomogeneous B -field: F = -grad E = grad ( m B ) (7.6) Magnetic susceptibility χ mag : M = χ mag H (7.7) B = µ 0 ( H + M ) = µ 0 (1+ χ mag ) H (7.8) 1+ χ = µ : permeability χ mag = µ -1 (7.9) M = χ mag H = ( µ - 1) H (index mag often omitted) (7.10) χ , µ : generally symmetric tensors, here: only isotropic media and cubic crystals. Diamagnetism:
7-3 χ < 0 µ < 1 Magnetization opposite to applied field χ << 1 µ 1 e.g., Cu: χ = -7 × 10 -6 Generally χ = M/H = const.

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