Force as gradient of potential function

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Discussion Overview

The discussion revolves around the concept of force as the gradient of a potential function, particularly in the context of equipotential surfaces. Participants explore whether different points on an equipotential surface can exhibit varying force field strengths, using examples from electrostatics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions if two points on an equipotential surface can have different force field values due to varying spacing of equipotential lines.
  • Another participant agrees and provides an example of an electric dipole, noting that the electric field strength varies along the surface between the charges.
  • Several participants request additional examples to clarify the concept further.
  • A participant mentions a charged metal needle, suggesting that the electric field strength is higher at the sharp point compared to the middle, and discusses the relationship between surface curvature and field line density.
  • There is a clarification that higher local density of field lines does not necessarily equate to higher energy, as potential remains constant.
  • A participant reflects on a previous misunderstanding regarding the relationship between surface area and field line density.

Areas of Agreement / Disagreement

Participants generally agree on the concept that force can vary on equipotential surfaces, but the discussion includes multiple examples and interpretations, indicating that there is no consensus on all aspects of the topic.

Contextual Notes

Some assumptions about the nature of electric fields and equipotential surfaces may not be fully explored, and the relationship between field line density and energy is presented with some ambiguity.

JP O'Donnell
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Hi.

Is it possible for two separate points on an equipotential surface to have two different values for the force field?

eg, point A and point B lie on an equipotential surface, but the equipotential surface spacing is much denser at A than at B - so the force field at A as the gradient of the potential must be greater than that at B?

Is this right?
 
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Yes, you're right.

A good example is to think about a dipole, and the line (really a surface) that runs halfway between them:

Code:
        O
        |
<-------+------->
        |
        O

The electric field changes as one moves along the horizontal line, and has a maximum when you are halfway between the charges.
 
thanks.
 
Thanks allot...but can anyone gives more examples for me please..
 
Alia Al-Hajri said:
Thanks allot...but can anyone gives more examples for me please..
What about a charged metal needle? At the sharp point E is a lot higher then in the middle. In general any surface having the smaller radius has the higher density of field lines. Mind you higher local density doesn't equate to higher energy, this is so because the potential is equal.
 
Per Oni said:
What about a charged metal needle? At the sharp point E is a lot higher then in the middle. In general any surface having the smaller radius has the higher density of field lines. Mind you higher local density doesn't equate to higher energy, this is so because the potential is equal.

Oh' ...Thank you..I really get the idea

I used to think that the surface area anything is a direct match with the density of field lines

So, That is not true!
 

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