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Identical conducting spheres share charge on contact: the new Coulomb force

This type of question, asked 3 times: 29 Jul 2022, 6 Apr 2024, 24 Jan 2025. All 3 questions below, oldest first.

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  1. Question 1

    29 Jul 2022

    91
    Two identical metallic spheres AA and BB when placed at certain distance in air repel each other with a force of FF. Another identical uncharged sphere CC is first placed in contact with AA and then in contact with BB and finally placed at midpoint between spheres A and B. The force experienced by sphere CC will be:

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  2. Question 2

    6 Apr 2024

    98
    Two identical conducting spheres PP and SS with charge QQ on each, repel each other with a force 16 N16\text{ }N. A third identical uncharged conducting sphere RR is successively brought in contact with the two spheres. The new force of repulsion between PP and SS is :

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  3. Question 3

    24 Jan 2025

    93
    A small uncharged conducting sphere is placed in contact with an identical sphere but having 4×10−84 \times10^{- 8} C charge and then removed to a distance such that the force of repulsion between them is 9×10−3 N9 \times10^{- 3}\text{ }N. The distance between them is (Take 14πε0\frac{1}{4\pi\varepsilon_{0}} as 9×1099 \times10^{9} in SI units)

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