Electrostatic Potential Minimum: Equilibrium for Positive or Negative Charges?

[phantom113]

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.

 

[LowlyPion]

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?

 

[AEM]

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?

 

[phantom113]

Yes very much. Thanks.