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Wire #2 will experience a magnetic field of Eq.(1.6) due to wire #1 given by
It is a good exercise to show that if the wires were carrying currents in the opposite directions that the resulting forces will have the same magnitude as in Eq.(1.11) but are such as to cause a repulsion between the wires.
This force between two current carrying wires gives rise to the fundamental definition of the Ampère:
If two long parallel wires 1 m apart each carry a current of 1 A, then the force per unit length on each wire is 2 x 10- 7 N/m.This definition of the Ampère then gives rise to the basic definition of the unit of charge, the Coulomb:
A wire carrying a current of 1 A transports past a given point 1 C of charge per second.This definition also explains the reason why the constant of Eq.(1.7) was given exactly as 4 x 10- 7 T m/A.