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Electric Field in a Square Problem

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data

    I think it would be better if I put the picture.

    nTzgs.png

    Additional questions:
    Find the direction of the electric field.
    Find the magnitude of electric field due at C due to charges A, B, and D.

    Oq2YY.png


    2. Relevant equations

    Pythagorean Theorem.
    E = kq/r^2

    3. The attempt at a solution

    For the first problem, I drew vector diagrams based on the charges at the center of the square. I ended up having 4 arrows:
    O -> A (electron attraction)
    O -> D (electron attraction)
    O -> A (proton repulsion of charge C)
    O -> D (proton repulsion of charge D)
    So basically I had 2 visual arrows of pointing NW and SW from the origin. This makes the direction of the electric field to be West. Thats basically the part I only got.
    For the magnitude of the electric field I used E = kq/r^2 . I know r = [√(2)/2]a. Now I got lost on what to really do (I tried a bunch of stuff but it didn't really make sense to me). The final answer for the first question is 4√2 kq/a^2
     
  2. jcsd
  3. Sep 6, 2012 #2

    CWatters

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    Science Advisor
    Homework Helper

    Do you know how to sum vectors? eg Work out the x and y component of each vector. Sum all the x components and sum all the y components etc

    To further simplify the equations it might help to remember that:

    This is a square so 45 degree angles are involved.
    cos(45)=sin(45)=0.5*SQRT(2)
    Pythagorous involves squares and square roots

    sorry if you know all that.
     
  4. Sep 6, 2012 #3
    Thanks for the reply!

    All along I was doing my math wrong on adding the electric field vectors.

    As r = (sqrt2/2)a

    e = kq/(r^2)
    e = kq/(a^2/2)
    e = 2kq/(a^2) for each vector on one side.

    Since theres 2 vectors on each side then it equals to 4kq/(a^2)

    Combining the vectors using parallelogram rule I get 4sqrt2 kq/(a^2)

    For the third question (Find the magnitude of electric field due at C due to charges A, B, and D):
    Do I just solve this problem similar to the 1st question? (draw vectors based on the center O). I drew the vectors due to C and heres what I came up with:

    C -> A
    C -> D
    B -> down

    Not sure if I'm starting this correctly. Do I just add the electric field vectors again based on the superposition rule? If so how would I do the vector pointing north from B (not sure what I would put for as r).
     
    Last edited: Sep 6, 2012
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