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7 July, 03:35

A charge q1 of - 5.00 * 10-⁹ C and a charge q2 of - 2.00 * 10-⁹ C are separated by a distance of 40.0 cm. Find the equilibrium position for a third charge of + 15.0 * 10-⁹ C.

P. S. 10-⁹ is 10^-9

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  1. 7 July, 04:29
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    The equilibrium position will be in between q₁ and q₂.

    Let this position of third charge be x distance from q₁

    q₁ will pull the third charge towards it with force F₁

    F₁ = 9 x 10⁹x 5 x 10⁻⁹x15 x 10⁻⁹ / x²

    = 675 x 10⁻⁹ / x²

    q₂ will pull the third charge towards it with force F₂

    F₂ = 9 x 10⁹x 2 x 10⁻⁹x15 x 10⁻⁹ / (.40-x) ²

    = 270 x 10⁻⁹ / (.40-x) ²

    For equilibrium

    675 x 10⁻⁹ / x² = 270 x 10⁻⁹ / (.40-x) ²

    5 / x² = 2 / (.40-x) ²

    (.40-x) ² / x² = 2/5 =.4

    .4 - x / x =.632

    .4 - x =.632x

    .4 = 1.632 x

    x =.245.

    24.5 cm

    so third charge must be placed at 24.5 cm away from q₁ charge.
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