# Find the Potential energy of a system of charges

• Jaccobtw
In summary, the incorrect answer was zero, and the student did not appear to understand the symmetry of the equation.
Jaccobtw
Homework Statement
3 electrons and a proton are arranged in a regular tetrahedron with a side length of 10nm. What is the total electrostatic potential energy of this configuration? Assume the energy is zero when the electrons are infinitely far from each other. Give your answer in J
Relevant Equations
$$k \frac{q_1 q_2}{r}$$

There are six pairs. three turn out to be negative and three turn out to be positive (3q^2 - 3q^2) which nets zero when you add them together with the equation. But zero was the incorrect answer. Did I do something wrong? Thank you

Jaccobtw said:
But zero was the incorrect answer. Did I do something wrong?
You must have done. How did you try to calculate the PE?

PeroK said:
You must have done. How did you try to calculate the PE?
$$\frac{k}{r}(3q^2 - 3q^2)$$ which is zero.

PeroK
Jaccobtw said:
$$\frac{k}{r}(3q^2 - 3q^2)$$ which is zero.
What is that?!

PeroK said:
What is that?!
What's wrong? That's how you calculate the potential energy of a system of charges. You have 6 pairs. 3 of them are q^2 and 3 of them are -(q^2). You multiply them by k and divide by r and add them together to get an answer.

PeroK
I can't find anything incorrect with your calculation. How do you know that "zero" is incorrect?

Jaccobtw
Jaccobtw said:
What's wrong? That's how you calculate the potential energy of a system of charges. You have 6 pairs. 3 of them are q^2 and 3 of them are -(q^2). You multiply them by k and divide by r and add them together to get an answer.
Yes, sorry, I failed to see the remarkable symmetry with the 3:1 ratio.

Jaccobtw
PeroK said:
Yes, sorry, I failed to see the remarkable symmetry with the 3:1 ratio.
I didn't know symmetry was required.

kuruman said:
I can't find anything incorrect with your calculation. How do you know that "zero" is incorrect?
The homework says it was wrong, but oddly enough the homework has been wrong many times this year

PeroK said:
Yes, sorry, I failed to see the remarkable symmetry with the 3:1 ratio.
A fun exercise: find the solutions of m protons and n electrons with zero EPE when equidistant (in a space of at least m+n-1 dimensions, of course).

## 1. What is potential energy?

Potential energy is the energy that an object possesses due to its position or configuration in a system. It is the energy that can be converted into other forms of energy, such as kinetic energy, when the object moves or changes position.

## 2. How is potential energy related to a system of charges?

In a system of charges, potential energy is the energy that is stored in the electric field between the charges. The amount of potential energy is determined by the positions and magnitudes of the charges in the system.

## 3. How do you calculate the potential energy of a system of charges?

The potential energy of a system of charges can be calculated using the equation U = k(q1q2)/r, where U is the potential energy, k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.

## 4. Can the potential energy of a system of charges be negative?

Yes, the potential energy of a system of charges can be negative. This occurs when the charges in the system have opposite signs, resulting in an attractive force between them. In this case, the potential energy is negative because work is required to bring the charges together from an infinite distance.

## 5. How does the potential energy of a system of charges affect the behavior of the charges?

The potential energy of a system of charges affects the behavior of the charges by determining the direction and magnitude of the electric force between them. Charges will move in a way that minimizes the potential energy of the system, which can result in the charges either attracting or repelling each other.

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