Two long parallel conductors X and Y are placed vertically at a distance d apart. Conductor X carries a current I upwards and conductor Y carries a current 2I downwards. A third long conductor Z is placed parallel to both X and Y and between X and Y. If Z carries a current I upwards and is at a distance x from conductor X, then:

Step-by-step solution

The force per unit length between two parallel current-carrying wires is given by F = ₀ I₁ I₂ 2 r . Wires carrying current in the same direction attract each other, while wires carrying current in opposite directions repel each other. The force per unit length on wire Z due to wire X is: F_ ZX = ₀ I I 2 x = ₀ I^2 2 x Since the currents in X and Z are in the same direction (upwards), this force is attractive. Therefore, F_ ZX is directed towards X. The force per unit length on wire Z due to wire Y is: F_ ZY = ₀ I 2I