How is Coulomb's Law generalized for continuous charge distributions?

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Discussion Overview

The discussion focuses on the generalization of Coulomb's Law for continuous charge distributions, specifically how to calculate the force between them. It involves mathematical reasoning and integration techniques related to the force calculation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant proposes that the force can be expressed as F=kdqdq'/r^2 and questions whether to integrate first over dq' and then dq.
  • Another participant agrees that this approach works.
  • A different participant suggests that either dq or dq' can be integrated first, indicating flexibility in the integration order.
  • One participant emphasizes the importance of considering the vectorial nature of the force in the calculations.

Areas of Agreement / Disagreement

Participants generally agree on the approach to integrating the force expression, but there is no consensus on the order of integration or the implications of the vectorial nature of the force.

Contextual Notes

There are unresolved aspects regarding the implications of the vectorial nature of the force and how it affects the integration process.

basik156
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For calculating the force on a continuous charge distribution due to another continuous charge distribution, if F=kdqdq'/r^2 would you simply integrate first over dq' and then dq?
 
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That works, right.
 
Either dq or dq' can be integrated first.
 
basik156 said:
For calculating the force on a continuous charge distribution due to another continuous charge distribution, if F=kdqdq'/r^2 would you simply integrate first over dq' and then dq?

Don't forget to take into account the vectorial nature of F.
 

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