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Force on 1 point charge in a 4 point charge system

  1. Sep 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Four identical charges are placed at the corners of a square of side side L.
    Find the magnitude total force exerted on one charge by the other three charges.
    Express your answer in terms of the variables Q, L and appropriate constants.

    where did the L root2 in the solution come from?


    2. Relevant equations

    F=k(q1q2/r^2)





    3. The attempt at a solution

    let the charge Q at bottom left corner be considered, it is ready to move under repulsion

    f1 = F(top, bottom) = kQ^2/L^2 [south] = x
    f2=F(right, bottom) = kQ^2/L^2 [west] = x
    f3 = F(diagonal, bottom) = kQ^2/[L root2]^2 [south-west]
    f3 = x/2
    --------------------------------------…
    resolve f3 along south & west

    F(net south) = x + [x/2] cos 45 = x[1+ 1/2root2]
    F(net south) = x[1+2root2] /2root2 = F
    F(net west) = x[1+2root2] /2root2 =F

    F(resultant) = sqrt[F^2 + F^2] = F root2
    F(resultant) = [ x[1+2root2] /2root2 ][root2]
    F(resultant) = x[1+2root2] /2
    F(resultant) = kQ^2[1+2root2] /2L^2
     
  2. jcsd
  3. Sep 17, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    Use Pythagoras theorem to find the diagonal of the cube.
     
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