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Calculate the Electric Field at One Corner of a Square

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data
    One side of a square has length 2.0 cm.

    In three of the square's corners, there are point charges.
    Top left corner: -1.0 nC (call this A)
    Bottom left corner: 10 nC (call this B)
    Bottom right corner: -1.0 nC (call this C)

    The top right corner has no charge, and is labelled P.

    What is the magnitude of the electric field at point P?

    2. Relevant equations
    Electric Field = KQ/r2

    3. The attempt at a solution
    Electric Field Due to A:
    K(-1.0 x 10-9 C)/(0.02 m2) = -22475 N/C, left

    Electric Field Due to C:
    Same as above, but this time the direction is down

    Electric Field Due to B:
    First calculate the distance from B to P. This is 0.022+0.022 = 0.0008. Take the square root of 0.0008 to find 0.0282 m.
    K(10 x 10-9 C) / (0.0282)2 = 112375 N/C, at a 45 degree angle pointing north east.

    Now, take the sum of all three parts to find the net electric field.
    A and C together point south west, with a magnitude of 31784.44 N/C.

    112375 N/C - 31784.44 N/C = 80590.55 N/C, north east.

    However, the answer given on the page is not what I got. What went wrong?
  2. jcsd
  3. Feb 25, 2009 #2


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    Remember they add like vectors.
  4. Feb 25, 2009 #3
    I thought I did add them like vectors.

    Adding vectors A (points left) and C (points down) gives a new vector which points south west...

    22475^2 + 22475^2 = 1010251250.. take the square root of this and get 31784.44.

    Since this vector points the opposite direction as vector B, which is 112375, can't I go 112375 - 31784.44?
  5. Feb 25, 2009 #4


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    So you have. Sorry I just calculated it and I get (5 -√2)*22,500 = 80,680

    using k = 9*109

    So I can't say what they are looking for then.
  6. Feb 25, 2009 #5
    I get something similar, but I used K = 8.99x10^9. They are definitely looking for the electric field, but the answer given is 1.1 x 10 ^5.

    I think whoever wrote the answer sheet probably made a mistake.

  7. Feb 25, 2009 #6


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    Yes their mistake. They canceled out the -1 nC charges. They don't as described.
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