Two long straight parallel conductors carrying currents, exert a force on each other. Why ? Derive an expression for the force per unit length between two long straight parallel conductors carrying currents in opposite directions. Explain the nature of the force between these conductors.

Reason for exerting force on straight parallel conductors \(\displaystyle \frac{1}{2}\) Derivation for force per unit length $\displaystyle 2$ Explanation of nature of Force $\displaystyle 1$/$\displaystyle 2$ One conductor experiences a force due to magnetic field of the other conductor Magnetic field produced by conductor 'a' at all points along the length of conductor 'b' \[B_{a}=\frac{\mu_{0} I_{a}}{2 \pi d} \] Force on conductor 'b' due to this magnetic field \[\begin{aligned} F_{b a} & =I_{b} L B_{a} \\ F_{b a} & =\frac{\mu_{0} I_{a} I_{b} L}{2 \pi d} \end{aligned} \] \[f_{b a}=\frac{F_{b a}}{L}=\frac{\mu_{0} I_{a} I_{b}}{2 \pi d} \] directed away from a \[f_{a b}=\frac{F_{a b}}{L}=\frac{\mu_{0} I_{a} I_{b}}{2 \pi d} \] directed away from b Repulsive, the forces acting on them are away from each other.