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(D) Let the two wires be placed parallel to each other in the horizontal plane, separated by a distance $d$. Let the current $I$ flow through both wir

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At points halfway between the wires in the horizontal plane

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(D) Let the two wires be placed parallel to each other in the horizontal plane, separated by a distance $d$. Let the current $I$ flow through both wires in the same direction.At any point $P$ located exactly halfway between the wires, the magnetic field $B_1$ due to the first wire and $B_2$ due to the second wire can be calculated using the right-hand rule.Since the wires are parallel and carry the same current $I$ in the same direction, at the midpoint, the magnetic field $B_1$ points vertically upwards (or downwards depending on the direction of current), and $B_2$ points in the opposite direction.Specifically, $B_1 = \frac{\mu_0 I}{2\pi (d/2)}$ and $B_2 = \frac{\mu_0 I}{2\pi (d/2)}$.Since they are equal in magnitude and opposite in direction, the resultant magnetic field $B_{net} = B_1 - B_2 = 0$.At this point, because the net magnetic field is zero, the magnetic needle will not experience any torque and its orientation will be independent of the magnitude of the current $I$.

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