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442 ⏐⏐⏐ MAGNETIC CIRCUITS
I
N turns
I
10
9
8
7
6
5
4
3
2
1
0
µ (permeability) × 10 –3
µ
�
Steel
FIG. 11.20
Series magnetic circuit used to define the
hysteresis curve.
Cast steel
Sheet steel
300 600
Cast iron
900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500 H (At/m)
A
FIG. 11.19
Variation of m with the magnetizing force.
The flux density and the magnetizing force are related by the following
equation:
(11.8)
This equation indicates that for a particular magnetizing force, the
greater the permeability, the greater will be the induced flux density.
Since henries (H) and the magnetizing force (H) use the same capital
letter, it must be pointed out that all units of measurement in the text,
such as henries, use roman letters, such as H, whereas variables such as
the magnetizing force use italic letters, such as H.
11.8 HYSTERESIS
B � mH
A curve of the flux density B versus the magnetizing force H of a material
is of particular importance to the engineer. Curves of this type can
usually be found in manuals, descriptive pamphlets, and brochures published
by manufacturers of magnetic materials. A typical B-H curve for
a ferromagnetic material such as steel can be derived using the setup of
Fig. 11.20.
The core is initially unmagnetized and the current I � 0. If the current
I is increased to some value above zero, the magnetizing force H
will increase to a value determined by
H � � NID
�
l
The flux � and the flux density B (B ��/A) will also increase with the
current I (or H). If the material has no residual magnetism, and the
magnetizing force H is increased from zero to some value H a, the B-H
curve will follow the path shown in Fig. 11.21 between o and a. If the