Spindle Motor Control - Hard Disk Drive: Mechatronics and Control - page 206

Figure 4.1: Flux lines generated by a permanent magnet

4.1.2 Flux Density (Magnetic Induction)

Flux density is a vector, and is normally denoted by the symbol B. It describes
the magnetic fi elddistributioninthespaceandgives fl ux lines through a unit
area. The SI unit of the fl ux density is Tes la (T),orWeber per square
meter (Weber/m 2 ). In the electrical engineering, Gauss is also used as the
unit of fl ux density where 1 Gauss = 10 −4 Tes l a .
The relationship between the fl ux density and the fl ux can be described by

Z

B.dS.

Φ = (4.1)

S

B is the

In the equation, S is the area where the fl ux lines going through, and

fl ux density at the local area d S.
In the electric machine analysis, the fl ux density is very import in analyzing
the local fi eld effects, e.g., the magnetic saturation at a point, and the leakage
fi eld in a local area.

4.1.3 Magnetic Field Strength, Permeability and Rela-
tive Permeability

Magnetic fi eld strength is a vector, and is normally denoted by the symbol
H. It describes the intensity of magnetic fi eld. The SI unit of magnetic fi eld
strength is Ampere per meter (A/m). Oersted (Oe) is also used in engi-
neering as an alternative unit, and 1Oe = 10 3 /4π A/m.
Flux density and magnetic fi led strength are closely related. In vacuum, B
is proportional to H,

B = µ 0 H

(4.2)