Page 33 - Electric Machinery Fundamentals

INTRODUCTION TO MACHINERY PRINCIPLES 9

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Cross-sectional
area A

Mean path length fc

( FIGVREI-3
A simple magnetic core.

where H is the magnetic field intensity produced by the current InCl' and dl is a dif-
ferential element of length along the path of integration. In SI units, J is measured
in amperes and H is measured in ampere-turns per meter. To better understand the
meaning of this equation, it is helpful to apply it to the simple example in Figure 1-3.
Figure 1-3 shows a rectangular core with a winding of N turns of wire wrapped
about one leg of the core. If the core i,s composed of iron or certain other similar
metals (collectively called jerromagHetic materials), essentially all the magnetic
field produced by the current will remain inside the core, so the path of integration
in Ampere's law is the mean path length of the core lc. The cunent passing within
the path of integration Iller is then Ni, since the coi1 of wire cuts the path of inte-
gration N times while carrying current i. Ampere's law thus becomes
(1- 19)

Here H is the magnitude of the magnetic field intensity vector H. Therefore, the
magnitude of the magnetic field intensity in the core due to the applied current is

(1- 20)

The magnetic field intensity H is in a sense a measure of the "effort" that a
current is putting into the establishment of a magnetic field. The strength of the
(
magnetic field flux produced in the core also depends on the material of the core.
The relationship between the magnetic field intensity H and the resulting mag-
netic flux density B produced within a material is given by
(1- 21)