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Finding The Effect of Several Electrics Fields

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data
    Four charged particles are at the corners of a square of side a as shown in the figure below. (Let A = 5, B = 2, and C = 7.)


    2. Relevant equations



    3. The attempt at a solution
    Well, I first found the electric due to each particle individually:

    [itex]\vec{E_A}=k_e\frac{5q}{a^2}\widehat{i}[/itex]

    [itex]\vec{E_B}=k_e \large[ \frac{2q~cos(45°)}{a^2}\widehat{i}+\frac{2q~sin(45°)}{a^2}\widehat{j}][/itex]

    [itex]\vec{E_C}=k_e\frac{7q}{a^2}\widehat{j}[/itex]

    Summing the effects of the each electric field together:

    [itex]\vec{E_{tot}}=k_e \large[(\frac{5q+2q\cos{45°}}{a^2}\widehat{i}+(\frac{2q \sin{45°}+7q}{a^2}\widehat{j}[/itex]

    After simplifying, I found the magnitude of the electric field at point q, that the three particles create, to be [itex]10.58 \cdot \frac{q}{a^2}[/itex]; however, the true answer is, [itex]9.59 \cdot \frac{q}{a^2}[/itex] What did I do wrong?
     

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    Last edited: Feb 2, 2013
  2. jcsd
  3. Feb 2, 2013 #2

    Doc Al

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    Staff: Mentor

    You did not include a diagram or describe what you are asked to find.
     
  4. Feb 2, 2013 #3
    Sorry. I just attached one.
     
  5. Feb 2, 2013 #4

    Doc Al

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    OK, what's the distance between B and q?
     
  6. Feb 2, 2013 #5
    Wouldn't it be [itex]\sqrt{2}a[/itex]?
     
  7. Feb 2, 2013 #6
    I figured it would be better to resolve the electric field of B into its components.
     
  8. Feb 2, 2013 #7

    Doc Al

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    Staff: Mentor

    Right.
    Nothing wrong with that, but you must use the correct distance to calculate the field.
     
  9. Feb 2, 2013 #8
    Well, to get from point B to point q, don't I have to go a units to right and a units north? What are the correct distances?
     
  10. Feb 2, 2013 #9

    Doc Al

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    You just gave the correct distance in your earlier post. Use it!
     
  11. Feb 2, 2013 #10
    Oh I see, I am mixing the idea of resolving charges and distances together.
     
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