Force Between Two Parallel Wires Carrying Current

Every current carrying conductor is surrounded by a magnetic field. It means that it will exert force on a nearby current carrying conductor. The force between two current carrying conductors placed parallel to each other is mutual and magnetic in origin. A current carrying wire has no net electric charge, and hence cannot interact electrically with another such wire.

Consider two parallel wires separated by distance r and carrying currents I₁ and I₂, respectively. The magnetic field due to one wire at a distance r from it is B₁. Similarly, the field due to second wire at a distance r from it will be B₂.

B₁ = µ₀I₁/2πr

B2 = µ₀I₂/2πr

These fields are perpendicular to the length of the wires and therefore the force on a length L, of the other current carrying conductor is given by

F = B I L = µ₀I₁/2πr x I₂L

Force per unit length

F/L = µ₀I₁I₂/2πr

The forces are attractive when the currents are in the same direction and repulsive when they are in opposite directions.