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Unformatted text preview: ) S B =
d£B
S
y the space
nd
Sq
mmidpoint
lar to B windings,
L0 c
its 0
Outside solenoid
S
b
E d lB = 2proil, inducing a a du (29.10)
dl
(See Examples turns
sense easier to A timedetermined by a righthandr from symmetry axis
ed from Faraday’sand Maxwell’s of current (28.15)
often
(toroid) law N 29.1–29.6.)
distance through
Bx = with and2is3>2 equations: isuse.changing magnetic ﬂuxrule. (See a stationary conductor,
dS E B
£
lacement current 2
ocurrent in the coil.
dt
dl
C
L
21x + a Examples 28.7–28.10.)
2
i D = POutside the space enclosed by the windings
(29.14)
m
B L 0 0 NI
(increasing) S
p
^
S
r
S
ying electric ﬁeld generates a displacement current is an induced Within theﬁeld E of nonelectrostatic S
of
dt electric 2 u enclosed by the windings, d l
Tightly
space E =
B=
1v : B2
(29.7)
(circular loop) wound toroidal solenoidthere
S
2
d £ B with N turns
2pr
e
S
which
as a
(toroid)
distance r from
E
he mf actsE = source of magnetic ﬁeld in exactly (29.3)E ﬁeld isunonconservative and axis
(displacement current)IdBysymmetry cannot be assoa
origin. This
r
C
Outside the spaceS
enclosed by the windings
BL0
I
so
ame
op f way as conduction current. The relationships
m0 NI
dt
S
947 (all or part
dB
S
ciated with a potential. (See Example 29.11.) of a closed loop moves in a
O Bx
M
z
S
B=
Magnetic
947
The magnet’s
induced
S
weenieldLenz’s law: materials: When that(28.17) materials are Semf Q encl tends to oppose or cancel out
multielectricquantity in electrostatics is electric S orpresent, the magnetization of the material causes
0u
tionF
damental x and magnetic ﬁelds states magnetic
2a Lenz’s law and theirSsources
B (29.18)
ﬁeld)
I
an induced current dA = always +
Change in B
E
motion causes a
an additional contribution called
IN
P
x
be stated compactly N circular loops) to B. For paramagnetic and diamagnetic materials, m0 is replaced in
in four equations,
S
P0
(center ofMagnetic materials: When magnetic C from present, theBx is often easier to
d and
the change that caused it. Lenz’s
be derived
M
negative. Charges ofexpressions by law=can m eachhere m isFaraday’s law magnetization of the use. K m is its
B
changing material and
magneticﬁeld they form a completeK
w
mS
xwell’s equations. Together theSsame sign repel m0 , materials arethe permeability of themagnetic material causes
947
S
(increasing) B0
(See ExamplesS29.7 and 29.8.)
and ﬁelds)
. for the relationship of E and B contribution toDisplacement currentfor E Maxwell’s materials, theA time susan additionalin an magneticB. For paramagneticis deﬁned as xfield through m0 Mreplaced in
(Gauss’s law and diamagnetic equations:1. is agnetic i = P d £ E
the total
(29.6)
E = vBL charge The to their systemSis
isserved;relative permeability. ﬁelds isolatedsusceptibility xm S
(29.14)S
ﬁeld,
m = Km +
G
d and
S the a
S
– a displacement current B K m D itsE dt
coil, inducing material £
Induced electric ﬁelds: by
varying B 0
ﬁeld generates
magneticﬁeld expressionsWhen an electricinduced by a
is
is
IB
(conductor with length L moves materials = Kemf ,is positive quantities; those of ddiamagnetic materiE
rces.
ceptibilities for paramagn...
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This document was uploaded on 03/13/2014.
 Spring '14

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