Page 53 - Electric Machinery Fundamentals

INTRODUCTION TO MACHINERY PRINCIPLES 29

-------t-+f-!r-H-+------ \l(or H )
Area :x hysteresis loss

(

FIGURE 1-13
The effect of the size of magnetomotive force excursions on the magnitude of the hysteresis loss.

proportional to the rate of change in the flux with respect to time. In equation
form,

_ drp
(1-35)
dt
where eind is the vol~age induced in the turn of the coil and cp is the flux passing
through the turn. If a coil has N turns and if the same flux passes through all of
them, then the voltage induced across the whole coil is given by

drp
_N (1-36)
dt

where
eind = voltage induced in the coil
N = number of turns of wire in coil
rp ~ flux passing through coil

The minus sign in the equations is an expression of Lenz's law. Lenz's law states that
the direction of the voltage buildup in the coil is such that if the coil ends were short
circuited, it would produce cun'ent that would cause a flux opposing the original
flux change. Since the induced voltage opposes the change that causes it, a minus
sign is included in Equation (1-36). To understand this concept clearly, examine