Distance dependence in Ampere's force law

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Ampere's force law indicates that the force between two parallel conductors is independent of the distance between them, as expressed in the equation F=2ka(I1I2)/r. The force is measured in N/m, which reflects the force per unit length of the conductors rather than a total force. This distinction clarifies that while the distance (r) affects the force per unit length, the overall force remains constant for parallel conductors. The discussion highlights the importance of understanding the definitions and units involved in Ampere's law. Overall, the relationship emphasizes the unique characteristics of electromagnetic forces in this context.
Sunfire
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Hello,

In the Ampere's force law

F=2ka\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.
 
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Does it stem from the definition of Ampere
 
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 :)
 

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