Determining Electric Field at Origin Due to Charges A and B

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SUMMARY

The discussion focuses on calculating the electric field at the origin due to two charges, A and B, positioned in an equilateral triangle formation. Both charges A and B are initially positive (+Q) and located at a distance L from the origin. The electric field E is determined using the formula E = k*Q/r², leading to a result of √3 * k * Q / L², which arises from the vector addition of the electric field components and the angles in the triangle. The problem is solvable through algebraic manipulation and understanding of vector components.

PREREQUISITES
  • Understanding of electric field concepts and calculations
  • Familiarity with vector addition in physics
  • Knowledge of trigonometric functions, specifically in relation to angles in equilateral triangles
  • Proficiency in using Coulomb's law for electric forces
NEXT STEPS
  • Study vector addition techniques in physics
  • Learn about electric field calculations for multiple point charges
  • Explore the properties of equilateral triangles and their angles
  • Review Coulomb's law and its applications in electrostatics
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone studying electrostatics, particularly those tackling problems involving electric fields and vector components.

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Homework Statement


Determine the electric field E at the origin 0 in fig 16-56 due to the two charges at A and B. b.) Repeat, but let the charge at B be reversed in sign. I can;t find the figure online, so I'll have to describe it. Charge A is on the vertical axis distance L from the origin with charge B to the lower right at a distance of L which is also a distance of L from the origin. The origin, Charge A, and Charge B form an equilateral triangle. Charge A and B for the first part are both +Q.

Homework Equations


E=k*Q/r^2
tan^-1(y/x) = theta

The Attempt at a Solution


I understand that the electric field has to be calculated then the components added as vectors, and I understand how the answer in the back of the book was set up, except that the answer is the square root of 3 times k*q/L^2. I don't see how they could have gotten the square root of three with so little detail in the problem, but I'm assuming it has something to do with the angle between them? I've finished all my other more advanced problems but I'm still stumped by this one. Once I get the components I'll be able to calculate the angle, but I'm wondering how they got what they did. Thanks, all help is appreciated! Again, sorry for lack of diagram.
 
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Notice that they tell you that the charges form an equilateral triangle with the origin. What are the angles of an equilateral triangle equal to?

Assuming I am picturing this correctly, you should be able to use this information to get the components in terms of just q and L.
 
Thanks, but I got it in school today. Wasn't very hard, but took a bit of algebra and vector addition. Thanks anyway!
 

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