Two long straight parallel conductors carrying currents, exert a force on each other. Why? Derive an expression for the force per unit length between…

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.