Electrostatic force between two arbitrary shapes

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Discussion Overview

The discussion focuses on calculating the electrostatic force between charged surfaces with non-standard shapes, particularly exploring the application of existing formulas for parallel capacitor plates to these scenarios. Participants consider methods for approximating forces between segments of surfaces and specifically address the challenges posed by conical shapes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes breaking the total surface into segments with common shapes to calculate the electrostatic force, questioning whether the total force can be obtained by simply adding the forces from each segment.
  • Another participant cautions that forces are vectors and should be added by their Cartesian components rather than arithmetically.
  • A participant expresses uncertainty about manipulating the case of two conical surfaces and seeks further suggestions.
  • Another participant notes that the vertex of a cone is not smooth, which may complicate calculations.
  • One participant mentions that charge density increases near the edge of a cone and suggests that quantifying this density could facilitate force calculations, but they also note the absence of a specific formula for this scenario.

Areas of Agreement / Disagreement

Participants express differing views on the approach to calculating forces, particularly regarding the treatment of vector addition. There is no consensus on how to handle the complexities introduced by conical shapes or on the existence of a formula for calculating forces between such surfaces.

Contextual Notes

Participants acknowledge limitations in their approaches, including the neglect of mutual interactions between segments and the challenges posed by the geometry of conical surfaces. There is also uncertainty regarding the quantification of charge density near sharp edges.

yiorgos
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I am looking some help on applying the well known formula of the electrostatic force between two parallel capacitor plates on charged surfaces which have non usual shapes.
My approach is to break apart the total surface into segments with common shapes
and calculating the force between each two of them. Although this approach neglects the mutual interaction among one segment with all the others I think it would result in an acceptable approximation. My question is if the total force is given by arithmetically adding all the single forces or it is more complicated.

My second and more important for me question is how to calculate the force between two surfaces when the shape of one or both of them is that of a cone. I already know that at sharp surfaces the charge concentration is increased but I can't find any formula for calculating it.

Third and last, for two given surfaces, which are the shapes resulting in the greatest electrostatic force between them?

Thanks in advance for your time
 
Last edited:
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yiorgos said:
I am looking some help on applying the well known formula of the electrostatic force between two parallel capacitor plates on charged surfaces which have non usual shapes.
My approach is to break apart the total surface into segments with common shapes
and calculating the force between each two of them. Although this approach neglects the mutual interaction among one segment with all the others I think it would result in an acceptable approximation. My question is if the total force is given by arithmetically adding all the single forces or it is more complicated.

This is not really an answer, just a note of caution. Forces are vectors, so you can't add them arithmetically. Break them into the three Cartesian components, and add those arithmetically.
 
Thanks for your reply.
You are right, I had in mind the parallel plate case where all forces are parallel.

But still I can't figure out how to manipulate the case of the cone (two cones).
Any suggestions on this?
 
I will really have to think about that one. If anything comes to my mind, I'll let you know. The vertex of the cone is not smooth...
 
That's why the charge density is increased as we get closer to the edge.
If you can quantify the above density then you can relatively easy calculate
the force between them.
But as I said I can't find any formula of calculating that.
 

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