12.4.4 Demagnetizing and Depolarizing Factors
The theory of demagnetizing and depolarizing factors (Osborn, 1945) is useful in gaining
an appreciation of how the interior ?¬?elds of an object differ from the ?¬?elds exterior to that
object, and for calculating useful properties of magnetic cores.
When an ellipsoidal shape as illustrated in Figure 12.3 of dielectric or soft magnetic
material is introduced into a region in which there was previously a spatially uniform
electric ?¬?eld E or magnetic ?¬?eld H caused by some distribution of sources (charges or
currents), and these sources do not vary as a result, the material becomes uniformly
polarized with a polarization vector P or magnetized with a magnetization vector M.
That polarization or magnetization causes on the surface of the shape induced surface
charge densities or magnetic pole densities which make an additional contribution Ed or
Hd to the ?¬?elds interior to the shape. These ?¬?elds are in a direction opposite to the original
applied ?¬?elds Ea or Ha and tend to depolarize or demagnetize the material, and hence
reduce (but not reverse in direction) the polarization or magnetization in the interior of the
shape. The internal ?¬?elds E and H are also reduced.
The depolarizing or demagnetizing ?¬?elds are given by
E dx
E dy
E dz
24
35
??
1
?«0
Nx 0 0
0 Ny 0
0 0 Nz
24
35
Px
Py
Pz
24
35
,
H dx
H dy
H dz
24
35
??
Nx 0 0
0 Ny 0
0 0 Nz
24
35
Mx
My
Mz
24
35
,
where Nx, Ny, or Nz are known as depolarizing or demagnetizing factors.
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