# Potential Energy system of 3 charged particles

• irishetalon00
In summary, the conversation was about a test question regarding a system of 3 charged particles and the potential energy of the system. The question was whether the potential energy had decreased, increased, or stayed the same in a different arrangement of the particles. The answer was that the potential energy had increased. However, the person was stuck because they were unsure if the definition of potential energy as the ability to do work meant that the first system had the higher potential energy. After further explanation, the person was able to figure out the answer.

#### irishetalon00

I simply can't wrap my head around a test question I received.

I'll relate it as best as I can remember:

"A system of 3 charged particles are arranged such that the total potential energy of the system is -200 J.
Then, consider the same 3 particles, arranged so that the potential energy of the system is -20 J.

Has the potential energy of the system decreased, increased, or stayed the same?"
The answer was : the potential energy increasesLet me explain why I'm stuck. Here's what I understand.

I understand that the number -200 is smaller than -20. If you look at it like that, then the answer is the energy of the system has increased.

But Potential energy = the ability to do work.

Considering that definition, the first system has the greater ability to do work, and thus has the higher potential energy, in which case the going from the first to the second system is a decrease in the ability to do work, and is therefore a decrease in the potential energy.

Your help is greatly appreciated, this question blindsided me and I feel like the timeline of my learning is on hold until I can overcome this hurdle!

Last edited:
irishetalon00 said:
Considering that definition, the first system has the greater ability to do work, and thus has the higher potential energy,
Why do you say that?

I don't know! haha

Both Work and Potential Energy are scalars. So a higher magnitude in potential energy represents a higher ability to do work.

no?

No. Just because something is a scalar does not mean that its sign can be ignored.

I figured it out.

Thanks for the friendly and helpful response! :tongue:

Without your disparagement, no progress was possible!

irishetalon00 said:
Without your disparagement, no progress was possible!

## 1. What is potential energy in a system of 3 charged particles?

Potential energy is the energy stored in a system of 3 charged particles due to their positions and interactions with each other. It is a measure of the work that is required to move the particles from their current positions to a different configuration.

## 2. How is potential energy calculated in a system of 3 charged particles?

The potential energy in a system of 3 charged particles can be calculated using the formula E = k(q1q2/r12 + q1q3/r13 + q2q3/r23), where k is the Coulomb's constant, q1, q2, and q3 are the charges of the particles, and r12, r13, and r23 are the distances between the particles.

## 3. How does the distance between the particles affect the potential energy in a system of 3 charged particles?

The potential energy in a system of 3 charged particles is inversely proportional to the distance between the particles. This means that as the distance between the particles increases, the potential energy decreases, and vice versa.

## 4. Can the potential energy in a system of 3 charged particles be negative?

Yes, the potential energy in a system of 3 charged particles can be negative. This occurs when the particles have like charges and are repelling each other, leading to a decrease in potential energy.

## 5. How does the arrangement of charges affect the potential energy in a system of 3 charged particles?

The arrangement of charges can greatly affect the potential energy in a system of 3 charged particles. If the charges are arranged in a way that minimizes their interaction (such as a balanced triangle), the potential energy will be lower compared to an arrangement where the charges are closer together and experience stronger interactions.