Electrostatic Potential Minimum: Equilibrium for Positive or Negative Charges?

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Homework Help Overview

The discussion revolves around the concept of electrostatic potential and its relation to equilibrium points for positive and negative charges. Participants are exploring whether a minimum in electrostatic potential indicates stable equilibrium for different types of charges.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the definition of an equilibrium point in the context of electrostatic potential. Others suggest using analogies, such as a marble in a bowl, to illustrate the behavior of charges at potential minima.

Discussion Status

The discussion is ongoing, with participants actively seeking clarification on the concepts involved. An analogy has been provided to help illustrate the differences in behavior of positive and negative charges at a potential minimum, which has been acknowledged as helpful by one participant.

Contextual Notes

There is a noted lack of clarity regarding the definition of equilibrium points in electrostatics, and participants are working through this conceptual challenge without a definitive resolution yet.

phantom113
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Homework Statement



Suppose that the electrostatic potential has a minimum at some point. Is this an equilibrium point for a positive charge? For a negative charge?

I simply don't understand what the question is asking - what is an equilibrium point? A restatement would be terrific.

Thanks.
 
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If the field lines are ⊥ to the equipotential surfaces, and if you have a minimum at some point in the field, won't there be field lines pointing from more positive potentials toward the minimum? Which kind of charges travel along field lines from higher to lower E field equipotential surfaces?
 
phantom113 said:

Homework Statement



Suppose that the electrostatic potential has a minimum at some point. Is this an equilibrium point for a positive charge? For a negative charge?

I simply don't understand what the question is asking - what is an equilibrium point? A restatement would be terrific.

Thanks.

Let's use an analogy. suppose you had a hemispherical bowl and a marble. With the concave side of the bowl up if you placed the marble in the bottom and then pushed it to the side a little it would roll back. On the other hand if the bowl had the convex side up and you placed the marble on the top and then nudged it a bit it would roll off.

Well your electrostatics problem is like that. for charge of one sign the minimum of the electrostatic potential acts like the bowl is concave up and if you nudge the charge a little, it "sinks to the bottom". For charge of the other sign the minimum of the electrostatic potential acts like the bowl is upside down. If you nudge the charge a bit it will move off.

Does that help?
 
Yes very much. Thanks.
 

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