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Chapter 31
237
P31.71
The magnetic field produced by the current in the straight wire is
perpendicular to the plane of the coil at all points within the coil. The
magnitude of the field is
B
I
r
=
µ
π
0
2
. Thus, the flux linkage is
N
NIL
dr
r
NI
L
hw
h
t
B
h
Φ=
=
+
F
H
G
I
K
J
+
+
z
ωφ
00
22
max
ln
sin
bg
.
Finally, the induced emf is
FIG. P31.71
ε
µω
ππ
επ
φ
=−
+
F
H
G
I
K
J
+
×
+
F
H
G
I
K
J
+
+
−−
0
71
2
1
4
10
100 50 0 0 200
200
2
1
500
87 1
200
NI
L
w
h
t
t
t
max
ln
cos
..
ln
.
cos
.c
o
s
ej
a
fa
fa
f
a
f
m
s
cm
5.00 cm
mV
The term sin
t
+
in the expression for the current in the straight wire does not change
appreciably when
ω
t
changes by 0.10 rad or less. Thus, the current does not change appreciably
during a time interval
∆
t
<=
×
−
−
010
200
16 10
1
4
.
.
s
s
.
We define a critical length,
ct
∆=
×
×
=
×
−
3
0
01
0
1
61
0
4
81
0
84
4
.
ms
s
m
e
j
equal to the distance to
which field changes could be propagated during an interval of 16 10
4
.
×
−
s . This length is so much
larger than any dimension of the coil or its distance from the wire that, although we consider the
straight wire to be infinitely long, we can also safely ignore the field propagation effects in the
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Current

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