Page 34 - Electric Machinery Fundamentals
P. 34
10 ELECTRIC MACHINERY FUNDAMENTALS
where
H ~ magnetic field intensity
fL = magnetic permeability of material
B ~ resulting magnetic flux density produced
The actual magnetic flux density produced in a piece of material is thus
given by a product of two terms:
H, representing the effOIt exerted by the current to establish a magnetic field
p.,. representing the relative ease of establishing a magnetic field in a given
material
The units of magnetic field intensity are ampere-turns per meter, the units of per-
meability are henrys per meter, and the units of the resulting flux density are
webers per square meter, known as teslas (T).
The permeability of free space is called fLo, and its value is
7
1'-0 ~ 47T X 10- HIm (1-22)
The permeability of any other material compared to the pemleability of free space
is called its relative permeability:
- ~
IL,. - 1-10 (1-23)
Relative permeability is a convenient way to compare the magnetizability of
materials. For example, the steels used in modem machines have relative perme-
abilities of 2000 to 6000 or even more. This means that, for a given amount of
current, 2000 to 6000 times more flux is established in a piece of steel than in a
corresponding area of air. (The permeability of air is essentially the same as the
permeability of free space.) Obviously, the metals in a transformer or motor core
play an extremely important part in increasing and concentrating the magnetic
flux in the device.
Also, because the permeability of iron is so much higher than that of air, the
great majority of the flux in an iron core like that in Figure 1-3 remains inside the
core instead of traveling through the surrounding air, which has much lower per-
meability. The smaUleakage flux that does leave the iron core is very important
in determining the flux linkages between coils and the self-inductances of coils in
transformers and motors.
In a core such as the one shown in Figure 1-3, the magnitude of the flux
density is given by
(1-24)
(
Now the total flux in a given area is given by
'" ~ L • ciA (1-25a)
B
