Distance dependence in Ampere's force law

[Sunfire]

Hello,

In the Ampere's force law

F=2k_a$\frac{I_{1}I_{2}}{r}$

Ampere law,

the force between 2 parallel conductors doesn't seem to depend on the distance between them.

F is given in [N/m], instead of just [N]...

What is the rationale behind this?

Thank you.

 

[Sunfire]

Does it stem from the definition of Ampere

 

[Sunfire]

Reading some other threads on the subject helps... I see that the force is per unit of cable length, while r on the RHS is the distance betw the 2 cables, okay :)

 

[Sunfire]

This is a nice thread on the subject

https://www.physicsforums.com/showthread.php?t=397921