Unformatted text preview: etic in uni m are m mS where m v the permeabilityE the coil. small S
for l =
d
(29.10)
0
S
S S changing S
through a actsdA a conductor, current in
as =
iD
current)
dt
tegral
BF = q B 0 =
form B S relative permeability. The magnetic susceptibilitysourcedeﬁned as xm(29.19) exactly and(displacement S
ﬁeld,m0 Iand v both perpendicu ,ferromagnetic vmaterials,EKmagnetic ﬁeldm thanMagnetic susL encl magnetic ﬂux For whichstationary xmFis qof m is much= K in 1. unity
C larger
d The positive protons
(28.20)
S
alsBare l = negative quantities. and electriis
S small
A
+
Binduced
S
,etand electrons.ceptibilities induced electricmaterialsway small positive quantities; The relationships materi+
S
the sameCare Ias conduction –
there is an for paramagnetic ﬁeld E of permanent S B current. those for diamagnetic
cur lar to B and to Someother)
B increasing
a
q
S
not constant. each ferromagnetic materials are nonelectrostaticb K retaininglarger magnetizationis
r
+
als are small negative nonconservative and cannotdumagnets,m is much their than unity and S S
quantities. For (Gauss’s rlaw for beﬁelds)
ferromagnetic magnetic ﬁelds and their sources
materials,
E
B assof
bound togetherorigin. This ﬁeld is ﬁeld isnega (See LExamples 28.11 and 28.12.)
by the nuclear force; between electric and
the removed.
sitive
S
Q encl
S
even after theS
external magnetic
du
S
E
S
=
(29.18)
. greater than 1not nuclear size. Electric be stated compactly in four equations,
E=
v Magnetic ferromagnetic
(29.7)
ciated d l potential. can materials are permanent magnets, retaining their
h(See Point in :constant. aexternal magneticExample 29.11.)(See Examples 28.11 andcalled magnetizationE dAMagnitude
the B2with SomeField(See ﬁeld is removed. E = dlBL
P0
MagneticField
28.12.) (29.6) C
v
C even after the
d£E
Motional emf: If a conductor moves in a magneticS S
ﬁeld,
S
Maxwell’s equations. Together they form a S
complete
S
vS
of emf aalways tendsis induced. (See cancel out B
B
(all or part emf closed loop moves in a
of a and solids.
t oratoms, molecules,to oppose or Examples 29.9 and d l = m0 a i C +SP0withS b in B
(conductor Change L moves in unilength
S
dt encl
(Gauss’s law for E ﬁelds)
FieldBmotional
S
S
basis forC relationship of E and B ﬁelds to their
the
S
S
m
F = qvB
F = qE
form B ﬁeld, B and v both perpendicu0 I
L
rom Faraday’s
to use.
efasily; in ﬁeld) law and is often easiersources.
insulators, charge does not move eas29.10.)
S
+
d
–
Displacement current and Maxwell’s equations: A time toueach(29.20) £ E = v
S +S
Distance
lar to B and displacement B d z
¢u
du
d i D other)
a (29.14)
q
about insulators. r from conductor
b
=P
y
ls are
B dA = 0
(29.19)
vz 5 (increasing) az 5 2pr
displacement current
vz = varying electric ﬁeld generates a (Ampere’s law including dt
lim
=
(9.3)
dt
dt
L
current) G
C
ition
¢t S 0 £ B t
S
S
dt
S
d ¢ acts as a source of magnetic ﬁeld in exactlyS
S
Si
ya
which
S
EE
E=
1v B2(displacement current)
d l I At t (29.7)
E dl...
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This document was uploaded on 03/13/2014.
 Spring '14

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