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Small oscillations of a charge placed midway between two fixed charges

This type of question, asked 2 times: 2021 Paper 2, 27 Jul 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 2

    17
    Two electrons each are fixed at a distance 2d2d. A third charge proton placed at the midpoint is displaced slightly by a distance x(x<<d)x(x< <d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: ( m=m= mass of charged particle)

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  2. Question 2

    27 Jul 2022

    10
    Two identical positive charges QQ each are fixed at a distance of ' 2a2a ' apart from each other. Another point charge q0q_{0} with mass ' mm ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q0q_{0} executes SHM. The time period of oscillation of charge q0q_{0} will be:

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