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39. We refer to the (very large) wire length as
`
and seek to compute the ﬂux per meter: Φ
B
/`
. Using
the righthand rule discussed in Chapter 30, we see that the net Feld in the region between the axes of
antiparallel currents is the addition of the magnitudes of their individual Felds, as given by Eq. 3019
and Eq. 3022. 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 Feld at any point 0
<x<d/
2isthesameat
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/
2and
then multiplying by 2:
Φ
B
=2
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 Fall '08
 SPRUNGER
 Physics, Current

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