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Case 2: The same except that a straight circular constant-diameter
longitudinal hole is drilled through the length of the very long wire,
parallel to the wire, and the center of the hole is not at the center of
the original wire. As explained earlier, one can determine the magnetic
field at all locations, both inside and outside the space occupied by the
original wire, by the trick of using the field found for case 1 and the
field found for a smaller wire with position and dimension of the hole but
with current running in the opposite direction to case 1. One must of
course adjust the currents appropriately so that in the hole region the sum
of the currents of the thicker wire in what will be the hole region and the
thinner wire that fills the hole region is zero. Certainly the magnetic
field at all locations in space, both inside and outside the original wire,
will be different in case 2 than in case 1.
Bruce