Three Charges in a Triangle

[odesa]

Homework Statement

Three electrons form an equilateral triangle 1.00 nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?

Homework Equations

U = K q1 q2 / r
K = 9*10^9
q = 1.6*10^-19

The Attempt at a Solution

First I made the triangle and tried to get the U of the three negative charges. I did (9*10^9)(1.6*10^-19)^2/(1*10^-9) and multiplied this by 3 because there are 3 different PE combinations with the negative charges and got 6.912*10^-19. Then i found it for the positive and negative charges and there are also 3 combinations for this. I calculated the distance from the negative to the positive charge to be .66 nm and then i used the same formula multiplied by 3 to get 1.05*10^-8.

Now I tried adding the PE's together but the first number is negligible compared to the second. I'm not sure if I made a mistake in calculating the radius, or if there is another point I'm missing on how to figure out the total PE. Thanks in advance.

 

[anathema]

Thank you for your post. It seems that you have made a small mistake in your calculation. The distance between the negative and positive charges should be 1.00 nm, which is the length of one side of the equilateral triangle. This would give a potential energy of 3.84*10^-19 for the interaction between the negative and positive charges. When added to the potential energy of the negative charges, the total potential energy for the group of charges would be 1.26*10^-18.

I hope this helps. Please let me know if you have any further questions or if I can assist with anything else.

 

[Moetasim]

I would first commend the student for attempting to solve the problem using the correct equations and units. However, I would also point out that the approach used may not be the most efficient or accurate way to solve the problem.

To find the potential energy of the group of charges, the student should first calculate the potential energy of each individual charge with respect to the proton at the center of the triangle. This can be done using the equation U = K q1 q2 / r, where r is the distance between the two charges.

Next, the student should consider the potential energy of the electron-electron interactions within the triangle. Since the triangle is equilateral, all three sides have the same length of 1.00 nm. This means that the distance between each pair of electrons is also 1.00 nm. Using the same equation as before, the student can calculate the potential energy of each electron-electron interaction.

Finally, the student can add all the individual potential energies together to get the total potential energy of the group of charges.

It is also worth mentioning that the radius used in the calculation may not be accurate. The student should double check the distance between the charges to ensure that the correct value is used in the equation. Additionally, it may be helpful to draw a diagram to visualize the situation and make sure all the calculations are correct.

Overall, the student's attempt at solving the problem is a good start, but there may be some room for improvement in terms of accuracy and efficiency.