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Unformatted text preview: s law and is often easier toSuse.changing magneti
the change that caused B
rS
mple
m0 I changing magnetic Iopposite directions. The magnetic force of
currents are in ﬁeld, ¿motion of the loop,.in Magnetic Field
both.
S
field through the
B
currents and I (See their separation r or B deﬁnition
and ExamplesP29.7 and 29.8.)
The
B
Current Distribution
oint
MagneticFieldIMagnitudeS S
B=
(28.9)
S
B oil, inducing a
I
c
per unit length between the this relationship. (See Example
S
B
om a
2pr(See Examplesampere is based onconductors depends on their
the 29.1–29.6.)
B
S
B
S
c
coil
m0 I
B
currents I and ¿ and their separation The table lists magnetic ﬁelds caused by several current distributions. In each case the con urrent in the E
Magnetic ﬁelds due toI current distributions: r. The deﬁnition of
S
B
magS
E =I vBL
Distance r from conductor (29.6)
B=
B
tional emf: Long, straight conductor a magnetic.on this relationship. (See Example
If a conductor moves 28.5.)is based ﬁeld,
in
S
S
S
B
ductor the ampere current I
is carrying
2pr
B
netic
v
B
947
(conductor S S length L moves in uniwith
S
yB
otional emf is induced. Ia 228.5.)
nd
m0 (See Examples 29.9 and
S
B
irecCurrent Distribution (28.15)
PL and S
Magnetic Field
F = qvB
F = MagneticField Magnitude
qE
S
Bx =
form B ﬁeld, oint in v both 947
perpendicum0 Ia 2
10.)
o2
y
+
dl law of Biot and
The
m0 Ia 2 +
21 loop a 223>2 a
28.3
B =–
Circular x + of radius Magnetic ﬁeld of a current loop:SOn axis each other)
p
lar to B and to of loop
^
r
a
q
m
b 21 I
B
(28.15)0x 2 + a 223>2 S
of
Savart allows us to calculate the magnetic ﬁeld2 u conductorx =
proS
2
2 3>2
(circular loop) straight conductor
dl
Long, law: Lenz’s
Distance r from
B=
21x 2 oppose orLcancel outpr
Lenz’s Magnetic ﬁeld law the axisthat circular conducting2loopBof always tends + a 2
an
to
S
p2
Change in B
^
he
r
2
au Sr S
of a states loop: induced current or emf
m0 Ia
duced along current of a The law of Biot and d y S
S
m0 I (for N loops,ymultiply theseu
(circular loop)
(29.6)
E = vBL use.
2S
l
(29.7)
S
(28.15)
If a
ﬁeld,
the Savartradius a us to calculate the The ﬁeld dependsdon moves in a
Lenz’s I. = Atbe ﬁeldof loop
to
I magnetic derived
p
S B dB
m0 NI change that caused it.Motionallaw can1v conductor thedB Bx = magnetic 2 3>2 often easier B =
center
2
S
allows carrying current Eemf:C O : B2 profrom Faraday’s law and is
22 a
z
2a expressions a u
(28.17)
Bx = d £
(conductor=with m0 Ia I L dl by N) in uni u y S B
length moves r (increasing)
p2
x S the(See Examples 1x +and2
^
r
Circular loop of radius axis ofmotional conducting axis of loop
On of
29.9NI
ulti(See duced distanceax alongathe circular emf centerBclosedloop
along the
a axis (all or part of a loop I u
ed emf
m0
SB
S2
2a
m0 II ¿ B Examples 29.7 and 29.8.) Ifrom theis induced. ofloop moves in a loop)
dB
F
rs:
2
S
(circular
O x S2
21 + S 3>2
E=(29.3)
F
Bx =
form B (28.17)0xIandav2bothaperpendicudB u
ﬁeld,mL r z
= of N
(28.11)
29.10.) S ﬁeld) I the ﬁeld is
o the
radius ta carrying current thereB ﬁeld depends S P multite o...
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This document was uploaded on 03/13/2014.
 Spring '14

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