Force Between Two Parallel Current-Carrying Conductors

Two long parallel wires, separated by a distance d and carrying currents ia and ib.

Magnetic induction at every point of wire b due to current ia in wire a } = B_a = μ₀ i_a / 2_πd    ….(1)

According to the right hand rule, the direction of Ba is downward. Wire b, carrying the current ib, is thus situated in a magnetic field Ba perpendicular to its length. A length l of this wire experiences a magnetic force whose magnitude is

        F_ba = Ba ib l = μ₀ i_a i_b / 2_πd                    …. (2)

F_ba lies in the plane of the wires and points to the left.
    Force experienced by a unit length of the conductor} = F = μ₀ i_a i_b / 2_πd

Similarly, it can be shown that a unit length of wire a also experiences the same force but in the opposite direction. Thus the two wires should attract each other.
For anitparallel currents, the two wires repel each other.