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Unformatted text preview: f if (center pdt circular loops) ﬁeld point. If I. Theare NBloops, L on theS dBx x
S
S
y
tract
2a
I+
L
2r
Eu
B = to I (for N loops, multiply r
Long cylindrical conductor of radius R
Inside SThe magnet’sr 6 R
conductor,
m0 each Iother) I
S
I
theseP
lar to B and 2p R2I
x
S
a
plied by N.the the center of the loop,ofB= FloopB loop
At axis from the center x the0. (See
distance x along
m0 NI
lation CHAPTER
d
(center of N circular loops)
B=
center of
the
dBxB
I
F Atmotion causes a
O
z
N
(28.17) 2a expressions by N)x
Bx =
S
r
Example 28.6.)
to the ﬁeld point. If there are N loops, the ﬁeld is multia
u
force
2a
changing magnetic
Binduced
I
m0S I S
I
I
P
xS = 0. field through the 7 (center of N circular loops)E = S B S : 0B2r d l
G
d£
S
R
=
conductor, r
1v m I
(29.7) Bx x
uced electric ﬁelds: When plied byis induced center of the loop, Outside(SeeB
an emf N. At the by a
nth.
their
d
S
S Long cylindrical conductor of radius R
E B = 2pr
S
E d l = Inside inducing a r 6 R
 oil, conductor,
(29.10)
tegral
S
C
Example 28.6.) (28.20)
B d l = m Iencla stationary conductor,
2p R2
B dt S
nging
through S
tion ofmagnetic ﬂuxlaw: 0Faraday’s law states that the induced emf that cthe line the coil.
A
S
S
B
C states
I
cS Sin integral
urrentBd £ B
Ampere’s law: Ampere’s law
et cur Faraday’s
(28.20)a closed loop moves in a
S
0 Iencl
B=m
Long, closely wound of nonelectrostatic
Inside Er du B near center A B d l = m(29.3) (all orSpart of 0 nI
solenoid,
B= re is an induced electric ﬁeld E solenoid
S
mple
B increasing I
m
I
S
S
in a closed loop unit length, around any the time rate of r Outside the net
the near
f conductor, r
sitive ﬁeld isnnonconservative of B negative of closed path equals m0 times S dt curE7 = vBL
S
B ﬁeld) B = 0
(29.6)
R
E
with turns per equals and cannot be assomoves in a magnetic ﬁeld,
Motional emf: If a conductor
r du B S
in. This
S
S
dpath. The positive
u
2prThe magnet’s B r
S
S
fv
rentlaw:
through the area enclosed by the
E
dl
change of magnetic ﬂux through the loop. This relation. (See a potential. (See Example 29.11.)Ampere’s law states that the line integral
Ampere’s
L
Outside and
S
(conductor m0 IS length L movesBin unimotion causes a du
B d l = with
(28.20) 0
ed with its midpoint
S
a motional emf is change is(See Examples 29.9solenoid
N
encl
dl
sense induced.
S
ship is valid whether the ﬂuxsolenoid is caused by a by a righthand rule. (See A
B = m0 nI
Long, closelyaround of current path equals m0 times the solenoid, nearform B ﬁeld, L and S both perpendicuchanging mIagnetic = qvB B
Inside net curcenterS
of B wound any closed determined
F r du
F = qE
v
m0 NI
29.10.) ﬁeld,unit
S
S
r+
magnetic
motion the
field through the
f+
the
–
ent or emf changing withIatoroidalExamples 28.7–28.10.) orelectric ﬁelds: WhenBan emf is induced by a
always tends toturns throughlength,out Induced both. path. The positive
oppose or cancelofnear loop,
Tightly woundn 2rent persolenoid area enclosed by the WithinChange in enclosed by the and to each other...
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This document was uploaded on 03/13/2014.
 Spring '14

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