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(29.10)
BRIDGING, PROBLEM
Magnetic Field of a Charged,:Rotating Dielectric Disk
(Gauss’s
947
lar
1
uctor,
2
C At t
dt way conductionucurrent. Field of a Charged, Rotating Dielectric m Ia 2 law for B ﬁelds)
the same vz as dvz
¢
C
BRIDGING PROBLEM
MagneticSThe relationships S 2
Disk
d
0
d £ Bpart
S
(allS increasing a closed
atic
ular Onaz = betweenqelectric and magnetic ﬁeldsEandl their sources of inducedDuloop movesencla
d =  BorS
= in
axis lim 0
of loop =
S
S
S
S
dis A thin dielectric ƒ ¢1tq2with dt = a has a total charge +Sﬁeld)2 on 1B 4. (29.21) B Q it take the charge found in step£3 to make a
1S disk ƒ radius dt 2
E
dt F
¢t
BQ distribC
e assoS 2 3>2
How u2 = does
long
E dA
E
can be stated compactly in four (21.2) called
second F = A thin dielectric disk with radius a equations,charge + Q distrib 4. How long P 21it 2 +Ba dS(29.18) i C in step 3 E b make a
2 = found + P d to
has a total
does x take the chargem0 a
l
u1
0
uted uniformly over2its surface. It rotates n(Faraday’s law) about
(9.5), timestimes complete
(9.6) per per second
4pP0 r equations.surface. It rotatesform a second about Ccomplete trip around the rotating ring? Use this0 todtﬁnd the curuted uniformly over its Together they n
x around C rotating ring? Use this to encl
the
Maxwell’s
r complete trip S
MagneticField Magnitude ﬁnd the curangu Point in Magnetic Field
S
S
an axis an axis perpendicular to
perpendicular to the surface of the disk disk and passing (Gauss’s of the rotating ring. N l
and passing
O rent law rotating I (for
sely
rent of the for mﬁelds)
ring.
(29.20)
multiply these
basis
of surface of
their q
S
G
Induced electricfor Find the an emfthe ﬁeld at by acenter of S disk.
is E and the the
relatedAt = vBL center. the When magnetic induced B ﬁelds toS the dS 1disk.d £ BUse a result= E 0Section 28.5 oops, E
(29.6)
E center
through its ofﬁelds:
looprelationshipmagnetic ﬁeld at the centerEof the =  S5. 5. Use aB (29.10) Section 28.5 tolaw981 the displacement
from
eld,
l
1Find 2
through its center.
S
g the changing£ E + v ﬂux+ a t athe
result from (Ampere’sto determine themagnetic ﬁeld
determine
including magnetic ﬁeld
magnetic
u 1 du
= sources. t through
(9.11)
maI
timev dt that this ring produces at the center of by disk.
C
S
S F1 on 2 20 expressions the N)
for
(conductor S 0zlength Lz S stationary conductor, B
i D = P an 0 8.988 * 2ﬁeld N ofm > uni(29.14)
have Distance=r withelectric10 9moves2inC2
there isS dtinduced
E
B that2 this ring produces at the center of theincreasing
dA B 0
rrent
S
from conductornonelectrostatic
= result current) 5 to ﬁnd S disk. magnetic ﬁeld
q =your result from Sstep(29.19) Bthetotal magnetic ﬁeld
F = qvB
FCIntegrate
q
6. =6. EIntegrate your pr fromstep 5 ﬁnd the total
form P(constantand v both perpendicu4p B0 ﬁeld, L
ion.
SOLUTION GUIDEaGUIDE
SOLUTION
E
2
S
S
(displacement current)z only)
+
.ctly SI origin. This ﬁeld is nonconservative and cannot be assoIn
S
r
from rings m
with r from r =
r=
from– allall ringsB 0 I radiifrom S = 0 toE£ = a. .
lar towith a MasteringPhysics® study areaVideo Video Tutor solution.
and to eachstudy area for a for
other)
BSee potential. (See Example 29.11.)a Tutor solution. +
a
q (Gauss’s law forwith radii S
dr B a
ciated
ﬁelds)
hips
b
See MasteringPhysics®
r 29 SUMMARY 29 SUMMARY
0 29 SUMMARY # # 0 ARY # 29 SUMMARY
0 # # # # RY # 0 RY # # # #
The table lists magnetic ﬁelds caused by several current distributions. In each case the con#
# RY # # # # #
The table# lists magnetic ﬁelds caused by several current distributions. In each case the con# # # #
#
#
e lists magnetic ﬁelds caused by several current distributions. In each case the con...
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This document was uploaded on 03/13/2014.
 Spring '14

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