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Test charge on the perpendicular bisector of two equal charges: distance for the maximum force

The same question, asked 2 times: 29 Jun 2022*, 1 Feb 2023. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    29 Jun 2022

    93
    Two -point charges QQ each are placed at a distance dd apart. A third point charge qq is placed at a distance xx from mid-point on the perpendicular bisector. The value of xx at which charge qq will experience the maximum Coulomb's force is:

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  2. Question 2

    1 Feb 2023

    30
    Two equal positive point charges are separated by a distance 2a2a. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge q0q_{0} becomes maximum is ax\frac{a}{\sqrt{x}}. The value of xx is___