Derive a mathematical expression for the force per unit length experienced by each of two long current-carrying conductors placed parallel to each other in air. Hence define one ampere of current. Explain why two parallel straight conductors carrying current in opposite directions repel each other.
Solution
Conductor 1 produces field B1=2πdμ0I1 at conductor 2, so the force per unit length on conductor 2 is
ℓF=B1I2=2πdμ0I1I2.
\textbf{One ampere} is the current which in each of two infinite parallel wires 1m apart in vacuum gives 2×10−7N per metre. For \textbf{opposite} currents, applying F=IL×B (or Fleming's left-hand rule) reverses the force on each wire, so they push apart — the force is repulsive.
