What is the electric field strength at the center of the triangle?

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SUMMARY

The electric field strength at the center of an equilateral triangle formed by three rods, two charged at +19.0 nC and one at -19.0 nC, requires careful consideration of vector components. The formula for the electric field due to a point charge, E = (kq)/r², is essential for calculating the contributions from each rod. The user mistakenly assumed that the electric fields from the two positively charged rods cancel each other out entirely, which is incorrect due to their symmetrical arrangement. The correct approach involves calculating the net electric field by considering both the magnitudes and directions of the electric fields from all three rods.

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  • Understanding of electric field concepts and vector addition
  • Familiarity with Coulomb's Law and the formula E = (kq)/r²
  • Knowledge of symmetry in electric fields
  • Basic principles of charge distribution and line charge calculations
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  • Learn about the electric field due to finite line charges
  • Explore vector addition of electric fields in two dimensions
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Homework Statement



What is the electric field strength at the center of the triangle?

Three 13.0 -cm-long rods form an equilateral triangle. Two of the rods are charged to + 19.0 nC, the third to - 19.0 nC .

What is the electric field strength at the center of the triangle?



Homework Equations



E=(kq)/r^2 lambda=deltaQ/deltax



The Attempt at a Solution



I've attempted this problem about 4 times and got all different but wrong answers. In each attempt I figured that the electric fields created by the two positively charged rods cancel each other out everywhere (This is where I believe I have made my mistake) and that the electric field depends only on the negative charged rod. I also figured by symmetry that the components of the electric field to the left and right (x-axis I chose) cancel each other out and the only electric field felt at the center is downwards (Y-axis I chose).

Is my mistake based on that I figured the two positively charged rods cancel each others electric fields out? I'm looking for some tips and hints to get me on track for this problem.

Thank you.
 
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Okay, let's start with the expression for the electric field of a finite line of charge.
 
is it E line=(K)(2)absolutevalue(lambda)/r ?

=(k)(2)absval(Q/x)/r
 
That is for an infinite line of charge, what about a finite one, any ideas?
 

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