0195136047.pdf

PROBLEMS 497

11.2.5Consider the toroid shown in Figure P11.2.5(a)
made up of three ferromagnetic materials. Ma-
terialais nickel–iron alloy having a mean arc
lengthlaof 0.6 m; materialbis medium sili-
con steel having a mean arc lengthlbof 0.4 m;
materialcis cast steel having a mean arc length
lcof 0.2 m. Each of the materials has a cross-
sectional area of 0.002 m^2. Find the mmf needed
to establish a magnetic flux ofφ= 1 .2 mWb by
making use of the magnetization curves given in

Figure P11.2.5(b).

11.2.6The configuration of a magnetic circuit is given in

Figure P11.2.6. Assume the permeability of the

ferromagnetic material to beμ= 1000 μ 0. Ne-

glect leakage, but correct for fringing by increas-

ing each linear dimension of the cross-sectional

area by the length of the air gap. The magnetic

material has a square cross-sectional area of 4

cm^2. Find the air-gap flux density, and the mag-

netic field intensity in the air gap.

lb

lc

la

+

VN

(a)

R I

Figure P11.2.5(a)Toroid.(b)Magnetization curves of

typical ferromagnetic materials.

So

ft

ca

st

ste

el

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

10 20 30 40 60 80 100 200 300 400 600 1000 2000 4000 10,000

Magnetic flux density, T

Magnetic field intensity, At/m

Nic

kel–

iron

alloy

Me

diu

m

sili

con

she

ets

teel

Ca

st

iro

n