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208
Sources of the Magnetic Field
P30.65
The central wire creates field
B
=
µ
π
01
2
I
R
counterclockwise. The curved portions of the loop feels no
force since
A
×=
B
0 there. The straight portions both feel
I
A
×
B
forces to the right, amounting to
F
B
IL
I
R
IIL
R
==
2
012
2
2
to the right .
P30.66
I
rB
××
×
=
−
−
2
2
9 00 10
1 50 10
41
0
675
0
38
7
..
ej
e
j
A
Flow of
positive current is downward
negative charge flows upward
or
.
P30.67
By symmetry of the arrangement, the magnitude of the net magnetic field
at point
P
is
BB
x
=
8
0
where
B
0
is the contribution to the field due to
current in an edge length equal to
L
2
. In order to calculate
B
0
, we use the
BiotSavart law and consider the plane of the square to be the
yz
plane with
point
P
on the
x
axis. The contribution to the magnetic field at point
P
due
to a current element of length
dz
and located a distance
z
along the axis is
given by Equation 30.3.
B
r
0
0
2
4
=
×
z
I
d
r
A
±
.
FIG. P30.67
From the figure we see that
rxL
z
=+
+
22
2
4
and
dd
z d
z
Lx
z
A
=
+
++
±
sin
r
θ
2
4
4
.
By symmetry all components of the field
B
at
P
cancel except the components along
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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, Force

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