Force between Two Parallel Currents, the Ampere
Consider two long, straight, parallel wires separated by a distance a and carrying currents I1 and I2 in the same direction, as illustrated. We can determine the force exerted on one wire due to the magnetic field set up by the other wire. Wire 2, which carries a current I2, creates a magnetic fieldB2 at the location of wire 1. The direction of B2 is perpendicular to wire 1,the magnetic force on a length ℓ of wire 1 is F1 = I1ℓ x B2. Because ℓ is perpendicular to B2 in this situation, the magnitude of F1 is I1ℓB2. we see that
The direction of F1 is toward wire 2 because ℓ x B2 is in that direction. If the field set up at wire 2 by wire 1 is calculated, the force F2 acting on wire 2 is found to be equal in magnitude and opposite in direction to F1. This is what we expect because Newton’s third law must be obeyed. When the currents are in opposite directions, the forces are reversed and the wires repel each other. Hence, we find that parallel conductors carrying currents in the same direction attract each other, and parallel conductors carrying currents in opposite directions repel each other.
“When the magnitude of the force per unit length between two long, parallel wires that carry identical currents and are separated by 1 m is 2 x 10–7 N/m, the current in each wire is defined to be 1 A”.
