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March 25, 2017

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A point charge +6.7 uC is placed at the origin, and a second charge –3.6 uC is placed in the X - Y plane at (0.40 m , 0.55 m ). Where should a third charge be placed in the plane so that the net force acting on it is zero?

  • Physics - ,

    tanα=0.55/0.4 =1.375.
    α=54⁰
    The distance between the charges
    d = sqrt(0.4²+0.55²) = 0.68 m
    The electric field at the disired point is zero =>
    k•q₁/0.68+r)²=k•q₂/r²,
    0.86r²-1.36r-0.46=0,
    r ={1.36±sqrt(1.85+1.58)}/1.72 = >
    r₁=1.867 m , r₂= - 0.28 m (extraneous root)

    d+r=0.68+1.867=2.547 m
    x=2.547•cos54=1.5 m
    y=2.547•sin54=2.06 m.

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