Three electrons form an equilateral triangle

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SUMMARY

The discussion focuses on calculating the potential energy of a system consisting of three electrons arranged in an equilateral triangle with a proton at the center. The known variables include the side length of the triangle (1.00 nm), the charge of the proton (1.60 × 10-19C), and the charge of the electrons (-1.60 × 10-19C). The potential energy equation used is ΔU = (kq1q2)/r, where the distance r is calculated as 5.77 × 10-10m. A key error identified in the calculations is the incorrect handling of signs, which affects the final potential energy result.

PREREQUISITES
  • Understanding of electrostatics and Coulomb's law
  • Familiarity with potential energy calculations in electric fields
  • Knowledge of basic geometry, specifically equilateral triangles
  • Proficiency in algebra for manipulating equations
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  • Review the principles of Coulomb's law and electric potential energy
  • Study the concept of electric field strength and its relation to potential energy
  • Learn about the significance of sign conventions in physics calculations
  • Explore examples of multi-charge systems and their potential energy calculations
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This discussion is beneficial for physics students, educators, and anyone interested in electrostatics, particularly in calculating potential energy in systems with multiple charges.

t.kirschner99
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1. Homework Statement

Three electrons form an equilateral triangle 1.00nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?
Known Variables:
s = 1.00 × 10-9m
p+ Charge = 1.60 × 10-19C
e- Charge = -1.60 × 10-19C
r = s/√(3) = 5.77 × 10-10m

Homework Equations



ΔU = (kq1q2)/ r

The Attempt at a Solution


[/B]
ΔU = k[(3(-1.60×10-19)2))/(1.00×10-9) - ((3(1.60×10-19)(-1.60×-19))/(5.77 × 10-10))]

For some reason I cannot get the answer, and I was wondering if anyone could spot my error. Thanks!
 
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The term with denominator 5.77x10^-10 should be negative but you have a double minus sign which makes it positive. The potential energy of the proton due to the 3 electrons should be negative due to the attraction.
 

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