Two long straight parallel wires, carrying (adjustable) currents $$I_1$$ and $$I_2$$, are kept at a distance $$d$$ apart. If the force $$F$$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of $$F$$, on the product $$I_1 I_2$$, would be:

The force between two parallel wires is proportional to the product of their currents ($$F \propto I_1 I_2$$), where like currents attract and opposite currents repel.

Attraction: Occurs when $$I_1 I_2 > 0$$. The given convention defines this force as negative ($$F < 0$$).

Repulsion: Occurs when $$I_1 I_2 < 0$$. The given convention defines this force as positive ($$F > 0$$).

These conditions describe a linear relationship $$F = -k(I_1 I_2)$$, representing a straight line with a negative slope passing through the origin.

The only graph showing a negative slope through the origin is Option D.