43. We refer to the (very large) wire length as
A
and seek to compute the flux per meter:
Φ
B
/.
A
Using the righthand rule discussed in Chapter 29, we see that the net field in the
region between the axes of antiparallel currents is the addition of the magnitudes of their
individual fields, as given by Eq. 2917 and Eq. 2920. There is an evident reflection
symmetry in the problem, where the plane of symmetry is midway between the two wires
(at
x = d
/2); the net field at any point 0 <
x < d
/2 is the same at its “mirror image” point
d – x
. The central axis of one of the wires passes through the origin, and that of the other
passes through
x = d
. We make use of the symmetry by integrating over 0 <
x < d
/2 and
then multiplying by 2:
()
/2
00
22
2
da
d
B
a
B dA
B
dx
B
dx
Φ=
=
+
∫∫
∫
AA
where
d
= 0.0025 m is the diameter of each wire. We will use
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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, Current

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