3 Equal Charges in Equilateral Triangle - Find KE @ Inf

In summary, the conversation is about a question regarding a specific integral not working. The person provides the relevant equations and their attempt at a solution, but is unsure why it is not working. They also mention their model for solving the problem and ask for help.
  • #1
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Homework Statement



Question is attached.

I know there's a few ways to solve this, but I'm wondering specifically why my integral of F ds isn't working.

Homework Equations



F = k * q^2 / r^2
U = ∫ F ds
cos 30 = √3/2
s= rcos30

The Attempt at a Solution



U = 2 * cos 30 * k * q^2 ∫ 1/r^2 ds
U = √3 * k * q^2 ∫ 1/r^2 * √3/2 dr - (a to inf)
U = 3/2 * k * q^2 * 1/a
 

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  • #2
Any help would be appreciated. No one seems to be able to help me.
 
  • #3
I assume your model is to let all three move apart some small amount, symmetrically. dr will be the increase in distance between any pair, while ds is the distance each moves. If so, I get dr = ds √3, which does not seem to be what you have used.
 

What is the concept of 3 equal charges in an equilateral triangle?

The concept of 3 equal charges in an equilateral triangle involves three point charges placed at the vertices of an equilateral triangle, with each charge having the same magnitude. This is a commonly used scenario in electrostatics to understand the behavior of electric charges.

How do you calculate the kinetic energy at infinity for 3 equal charges in an equilateral triangle?

The kinetic energy at infinity for 3 equal charges in an equilateral triangle can be calculated using the formula KE = (3/4)(kq²)/a, where k is the Coulomb's constant, q is the magnitude of the charge, and a is the length of the side of the equilateral triangle.

What is the significance of finding the kinetic energy at infinity for 3 equal charges in an equilateral triangle?

Finding the kinetic energy at infinity for 3 equal charges in an equilateral triangle helps in understanding the energy distribution and stability of the system. It also provides insights into the force interactions between the charges and the equilibrium position of the system.

Can the kinetic energy at infinity be negative for 3 equal charges in an equilateral triangle?

No, the kinetic energy at infinity cannot be negative for 3 equal charges in an equilateral triangle. This is because the charges in an equilateral triangle are equally spaced and have the same magnitude, resulting in a symmetrical distribution of energy. Therefore, the kinetic energy at infinity will always be positive.

How does the kinetic energy at infinity change when the charges in an equilateral triangle are not equal?

When the charges in an equilateral triangle are not equal, the kinetic energy at infinity will also change. This is because the distribution of energy will no longer be symmetrical, and the force interactions between the charges will be different. The kinetic energy at infinity will be higher for larger charges and lower for smaller charges compared to 3 equal charges in an equilateral triangle.

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