Solution:
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In the figure two long current carrying wires have been shown. Each wire
carries a current
. In wire
1 the current is coming out of the page and in wire 2 the current is going into
the page. Separation between the two wires is d. We will calculate the magnetic
field at point P, which is at a distance R from the mid-point of
the line joining the two wires. We have fixed the coordinate system by
indicating the unit vectors
and
;

The magnetic field at P due to the wire 1 will be
to the line joining 1 to P, as shown in the figure. Using the expression
for the magnetic field due to a long current carrying wire, we have

The magnetic field at P due to the wire 1 will be
to the line joining 1 to P, as shown in the figure. Using the expression
for the magnetic field due to a long current carrying wire, we have

Therefore, the magnetic field at P due to the current carrying wires will be

Substituting the expression for
, we find

(b)
The direction of the magnetic field at P is along the vector
,
which is in the direction of the line
to the
line joining the two wires at the middle, as shown in the figure.
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