# Electrostatic Potential Minimum: Equilibrium for Positive or Negative Charges?

• phantom113
In summary, the question is asking if a point with a minimum electrostatic potential acts as an equilibrium point for a positive or negative charge. The analogy used is a hemispherical bowl with a marble, where the charge behaves similarly depending on the sign of the charge. For a positive charge, the minimum acts as a concave bowl, while for a negative charge, it acts as a convex bowl.
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.

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.

## 1. What is a restatement of problem?

A restatement of problem is a summary or rephrasing of the main issue or challenge that a researcher or scientist is trying to address in their study or experiment. It is often used to clarify the purpose and objectives of the research and to provide a clear focus for the study.

## 2. Why is it important to have a restatement of problem in a scientific study?

A restatement of problem helps to define the scope and boundaries of the study, making it easier for the researcher to stay focused and avoid getting sidetracked. It also helps to provide a clear direction for the study and ensures that the research is relevant and meaningful.

## 3. How do you write a restatement of problem?

To write a restatement of problem, start by identifying the main issue or challenge that your research is addressing. Then, rephrase it in a clear and concise manner, using specific and measurable language. It should be written in a way that clearly outlines the problem and its significance.

## 4. Can a restatement of problem change throughout the course of a study?

Yes, a restatement of problem can change as the research progresses and new information is discovered. As the researcher gains a deeper understanding of the problem, they may need to revise or refine their restatement of problem to accurately reflect the current focus of the study.

## 5. How does a restatement of problem differ from a research question?

A restatement of problem is a broader and more general statement of the main issue or challenge that a researcher is trying to address. It provides the overall context for the research. In contrast, a research question is a specific and focused inquiry that the researcher wants to answer through their study.

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