Summary
1.
The
righthand
rule
can
be
used
to
determine
th
e
dir
e
ction
of
th
e
magn
e
tic
fi
e
ld
produc
ed by
a
curr
e
nt.
This
is
illustrat
ed
in
Figure
15.2
on
page
719.
2.
Force
is
exerted
on
a
charge
moving
through
a
magnetic
field
according
to
the
equation
f
=
qu
x
B
Similarly
,
force
s
appear
on
a
currentcarr
y
ing
wir
e
imm
er
se
d
in
a
magnetic
fi
eld.
The
forc
e
on
an
incremental
length
of
wire
is
given
by
df
=
idl
X
B
3.
According
to
Farada
y'
s
law
of
induction,
volt
age
is
induc
ed
in
a coil
wh
en
it
s
magnetic
flux
linkag
es
change
with
time.
Similarly
,
voltag
es
ar
e
induced
in
conductors
that
cut
through
magnetic
flux lines.
We
can
determine
the
polarity
of
the
induced
voltage
by
us
ing
Lenz's
law.
4.
Magnetic
flux
den
s
ity
B
and
the
magnetic
field
intensity
Hare
related
by
B
=
p,H
where
p,
is
the
magnetic
permeability
of
the
material.
For
air
or
vacuum
,
p,
=
JLO
=
4rr
x
10
7
.
5.
According
to
Ampere
's
law
,
the
line
integral
of
H
around
a
closed
path
is
equal
to
the
algebraic
s
um
of
th
e
curr
e
nts
flowing
through
the
ar
ea
bound
ed
Problems
Section 15.1: Magnetic Fields
P15.1.
What
is
the
fundamental
cause
of
magnetic
fields?
P15.2.
Stat
e
th
e
righthand
rule
as
it
appli
es
to
a.
a
curr
e
ntcarrying
conductor
;
b.
a
current
carrying
coil.
P15.3.
State
Ampere's
law,
includin
g
the
reference
direction
s
for
the
currents.
Problems
751
by
the
path.
We
can
use
thi
s
law
to
find
the
field
around
a
long
straight
wire
or
in
s
ide
a
toroidal
coil.
6.
Practical
magnetic
device
s
can
be
approximately
analyzed
by
us
ing
circuit
concepts.
Magneto
motive
forces
are
analogous
to
voltage
sources
,
reluctance
is
analogous
to
resi
s
tance,
and
flux is
analogous
to
current.
7.
The
inductance
and
mutual
inductance
of
coils
can
be
comput
ed
from
knowl
e
dge
of
the
phy
si
cal
parameter
s
of
the
coils
and
the
core
on
which
they
are
wound.
8.
The
BH
relationship
for
iron
take
s
the
form
of
a
hy
s
tere
sis
loop
,
which
displays
saturation
in
the
neighborhood
of
1
to
2 T.
The
area
of
the
loop
rep
resents
energ
y
converted
to
heat
per
cycle.
Eddy
curr
e
nts
ar
e
another
caus
e
of
cor
e loss.
Energy
can
be
s
tored
in
magnetic
fi
e
ld
s.
In
a
magn
e
tic
circuit
consisting
of
an
iron
core
with
an
air
gap
,
most
of
the
energy
is
stored
in
the
gap.
9.
In
an
ideal
transformer
,
the
volta
ge
acros
s
each
coil is
proportional
to
it
s
number
of
turns
,
the
net
mmf
is z
ero,
and
the
power
efficiency is
100
percent.
10.
Equival
e
nt
circuits
for
real
tran
s
form
ers
ar
e
s
hown
in
Figures
15.28
and
15.29
on
pages
747
and
748
, respectively.
11.
Efficiency
and
regulation
are
important
as
pects
of
tran
s
former
operation.
P15.4.
State
Faraday's
law
of
magnetic
induction
and
Len
z's
law.
*P15.5.
The
magnetic
field
of
the
earth
is
approxi
mat
ely 3 x
10
5
T.
At
what
distanc
e
from
a
long
s
traight
wire
carrying
a s
teady
current
of
10
A is
the
field
equal
to
10
percent
of
the
earth
's field?
Suggest
at
least
two
way
s
to
help
reduce
the
effect
of
electrical
circuit
s
on
the
navigation
compass
in
a
boat
or
airplane.
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 Spring '09
 Mechatronics, Magnetic Field, Ron, hat, nd

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