Electric potential energy graph

[slft]

Homework Statement

I understand the concept of negative potential energy value because it's chosen to be 0 at infinity. So considering two positive charges, as separation r increases, the potential energy V decreases.

When there's one positive and negative charge, as r increases, V increases. So from the graph, curve one, the potential energy at b is larger than at a (less negative), which makes sense to me. But I'm confused when comparing curve 1 and 2, where curve 2 involves larger charges, some multiple of curve 1. If there are larger charges, the potential energy in curve 2 larger (less negative) than that in curve 1. For example, for the potential energy at b, shouldn't the potential energy in curve 2 larger than -5? Can we compare it directly like we do for the same curve? or do we have to look at the magnitude of the negative value? but if so, how come we can compare directly the potential energy in the same curve with the value on the graph, while we can't compare different curve directly?

Homework Equations

The Attempt at a Solution

 

[SammyS]

The change in potential energy in going from position a to b is larger for curve 2 than for curve 1. So all is wonderful !

 

[slft]

So the position of the curve doesn't really mean anything?

 

[SammyS]

For the most part the position doesn't matter except as you noted, that it's often chosen so that the potential goes to zero at infinity.

 

[rwisz]

I can help clarify the concept of electric potential energy and how it relates to the graph you are looking at. Electric potential energy is a measure of the potential for a system of charges to do work on each other. It is dependent on the distance between the charges and their magnitudes.

In the case of two positive charges, as you correctly stated, the potential energy decreases as the separation between them increases. This is because the charges are repelling each other and the work required to move them farther apart decreases. Similarly, in the case of one positive and one negative charge, the potential energy increases as the separation increases, as the charges are now attracting each other and the work required to move them apart increases.

Now, when comparing curve 1 and curve 2, it is important to note that the charges involved are different. While curve 1 involves two positive charges, curve 2 involves larger charges, possibly a multiple of the charges in curve 1. This means that the potential energy values on curve 2 will be larger in magnitude compared to curve 1, as the charges involved are larger and thus have a greater potential to do work on each other.

Therefore, when comparing the potential energy values at point b on the two curves, it is not accurate to compare them directly. Instead, we must consider the magnitude of the negative values. In this case, the potential energy at point b on curve 2 may be less negative than -5, but it is still larger in magnitude compared to the potential energy at point b on curve 1.

In summary, the potential energy values on a graph can be compared directly only when they are on the same curve, as they represent the potential energy of the same system of charges. When comparing different curves, we must consider the magnitude of the values, as the charges involved may be different. I hope this helps clarify your confusion.