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Physics

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Charge 2 × 10−18 C is on the y axis a distance 4 m from the origin and charge 9 × 10−18 C is on the x axis a distance d from the origin.
What is the value of d for which the
x component of the force on 9 × 10−18 C
is the greatest? The Coulomb constant is
8.98755 × 109 N · m2/C2.
Answer in units of m

  • Physics -

    The force of charges interaction is
    F = k•q1•q2/r^2 = k•q1•q2/(d^2+4^2) = k•q1•q2/(d^2+16).
    X- projection is
    Fx= k•q1•q2/(d^2+16) •cosα = k•q1•q2/(d^2+16) •d/(d^2+16)^1/2.
    We have to find the derivative of Fx.
    (Fx)´ = k•q1•q2[(d^2+16)^-3/2 – 3d• (d^2+16)^-5/2] = 0
    Solving this equation, we find d = 2.83 m

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