A charge +q is located at the origin, while an identical charge is located on the x axis at x = +0.91 m. A third charge of +3q is located on

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A charge +q is located at the origin, while an identical charge is located on the x axis at x = +0.91 m. A third charge of +3q is located on the x axis at such a place that the net electrostatic force on the charge at the origin doubles, its direction remaining unchanged. Where should the third charge be located?

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  1. Answer:

    Charge should be located at x = 0.7071m

    Explanation:

    We are given;

    r = 0.5m

    From coulombs law, we know that;

    F = k•q1•q2/r²

    k is electrostatic constant with a value of 9 x 10^(9) N.m²/C²

    Now force between q and q is;

    F1 = 9 x 10^(9)•(q²) /0.5² = 3.6 x 10^(10) q²

    Now force between q and 2q is;

    F2 = 9 x 10^(9)•(q x 2q)/r²

    F2 = 1.8 x 10^(10) q²/r

    Net force = F1 + F2

    F_net = 3.6 x 10^(10) q² + 1.8 x 10^(10) q²/r²

    To get the required location,

    F_net = 2F1

    Thus,

    3.6 x 10^(10) q² + 1.8 x 10^(10) q²/r² = 2(3.6 x 10^(10) q²)

    Divide through by q² to get;

    3.6 x 10^(10) + (1.8 x 10^(10))/r = 2(3.6 x 10^(10))

    (1.8 x 10^(10))/r² = (7.2 x 10^(10)) – (3.6 x 10^(10))

    (1.8 x 10^(10))/r² = 3.6 x 10^(10)

    r² = (1.8 x 10^(10))/3.6 x 10^(10)

    r² = 0.5

    r = √0.5

    r = 0.7071m

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