0N/C Electric Field at center of equilateral Triangle

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SUMMARY

The discussion focuses on calculating the electric field at the center of an equilateral triangle. Participants highlight that the symmetry of the triangle allows for a simplified approach, where the distances from the vertices to the center are equal, leading to cancellation of the electric field components. The initial attempts involved unnecessary calculations of distances and trigonometric ratios, which are not required due to the inherent symmetry of the configuration. The conclusion emphasizes that understanding the symmetry can streamline the solution process significantly.

PREREQUISITES
  • Understanding of electric fields and their vector nature
  • Familiarity with the concept of symmetry in physics
  • Basic knowledge of equilateral triangles and their properties
  • Ability to perform vector addition and cancellation
NEXT STEPS
  • Study the principles of electric field superposition in various geometrical configurations
  • Learn about vector components and their role in electric field calculations
  • Explore symmetry in physics problems to simplify complex calculations
  • Review trigonometric applications in physics, specifically in relation to electric fields
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding electric fields in symmetrical configurations, particularly in the context of electrostatics.

Painguy
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Homework Statement


tKAX86E.png


I got an answer as you can see in both pictures, but apparently it is wrong. What did I do?

Homework Equations





The Attempt at a Solution


In this picture I found the y components of the electric field at C. Since the bottom 2 are the same i just doubled one of the electric fields. I then set it equal to the electric
field from the top to cancel out the effect from the bottom.
sSu8bxW.jpg
 
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Somehow, you are not seeing that the distance from the all the vertices to the center is the same; you do not even have to compute what it is, it will cancel out.

Note there is a much simpler solution, using only the symmetry.
 
The distance from vertices to the center is the same since it is an equilateral triangle. Using that information you can easily solve the problem by summing up the electrical field intensities to 0 and the distances will apparently cancel out. You don't even have to mess with trigonometrical ratios here
 
Last edited:

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