Distance dependence in Ampere's force law

  • Context: Undergrad 
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    Force Law
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Discussion Overview

The discussion centers around the Ampere's force law, specifically examining the expression for the force between two parallel conductors and its dependence on distance. Participants explore the implications of the force being expressed in terms of force per unit length and the significance of the distance variable in the equation.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the rationale behind the force being expressed in terms of [N/m] rather than [N], suggesting a potential misunderstanding of the relationship between force and distance in the context of Ampere's law.
  • Another participant proposes that the expression may relate to the definition of the Ampere, implying a connection between the units and the physical interpretation of the law.
  • A different participant clarifies that the force is indeed per unit length of the conductors, indicating that the distance r refers to the separation between the two cables.
  • A participant shares a link to another thread, suggesting that further reading may provide additional insights into the topic.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express different levels of understanding and interpretation regarding the implications of the force per unit length and the role of distance in the Ampere's force law.

Contextual Notes

Participants have not fully resolved the implications of the units used in the force equation or the foundational definitions related to the Ampere, leaving some assumptions and interpretations open for further exploration.

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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