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Only the
x
components of the fields (contributed by each side) will contribute to the final
result (other components cancel in pairs), so a trigonometric factor of
a
R
a
ax
2
4
22
=
+
multiplies the expression of the field given by the result of Problem 2917 (for each side
of length
L = a
). Since there are four sides, we find
Bx
i
R
a
aR
a
ia
a
a
x
bg
b
g
e
j
b
g
=
F
H
G
I
K
J
+
F
H
G
I
K
J
+
F
H
G
I
K
J
=
++
+
4
2
44
4
24
4
2
4
0
0
2
2
2
2
2
µµ
π
π
1
2
which simplifies to the desired result. It is straightforward to set
x
= 0 and see that this
reduces to the expression found in Problem 2987 (noting that
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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