Page 54 - Electric Machinery Fundamentals

30 ELECTRIC MACHINERY FUNDAMENTALS

Direction of i required
"<--- "<---
- i
+
P
e;od (
Nturns

:- Direction of
,
opposing flux
If If ~ increasing
~ c----::>- -
(a) (b)
FIGURE 1-14
The meaning of Lenz's law: (a) A coil enclosing an increasing magnetic flux; (b) determining the
resulting voltage polarity.

Figure 1- 14. If the flux shown in the figure is increasing in strength, then the volt-
age built up in the coil will tend to establish a flux that will oppose the increase. A
current flowing as shown in Figure 1-14b would produce a flux opposing the in-
crease, so the voltage on the coil must be built up with the polarity required to drive
that current through the extemal circuit. Therefore, the voltage must be built up with
the polarity shown in the figure. Since the polarity of the resulting voltage can be de-
termined from physical considerations, the minus sign in Equations (1-35) and
CI-36) is often left out. It is left out of Faraday's law in the remainder of this book.
There is one major difficulty involved in using Equation (1-36) in practical
problems. That equation assumes that exactly the same nux is present in each turn
of the coil. Unfortunately, the flux leaking out of the core into the surrounding air
prevents this from being true. If the windings are tightly coupled, so that the vast
majority of the flux passing through one turn of the coil does indeed pass through
all of them, then Equation (1-36) will give valid answers. But if leakage is quite
high or if extreme accuracy is required, a different expression that does not make
that assumption will be needed. The magnitude of the voltage in the ith turn of the
coil is always given by
dC",;)
e· = -- (1-37)
, dt
If there are N tU111S in the coil of wire, the total voltage on the coil is
N
(1-38)
eind = :L e j
i =1
= ± d(",;)
(1-39)
1=] dt