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Potential at the centre of a symmetric arrangement of equal charges

This type of question, asked 4 times: 2 May 2023 S2, 3 May 2023 S2, 23 Apr 2025 S1, 20 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    45
    Four point charges each +q+q are placed on the circumference of a circle of diameter 2d2d in such a way that they form a square. The potential at the centre is proportional to

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  2. Question 2

    3 May 2023 S2

    4
    A regular hexagon of side 10 cm has a charge 1 μC1\,\mu\text{C} at each of its vertices. The potential at the centre of hexagon is [14πε0=9×109 SI unit]\left[\frac{1}{4\pi\varepsilon_{0}}=9\times10^{9}\text{ SI unit}\right]

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  3. Question 3

    23 Apr 2025 S1

    7
    A regular hexagon of side 6 cm has a charge of 2μC2\mu C at each of its vertices, what is the potential at the centre of the hexagon? [14πε0=9×109\frac{1}{4\pi\varepsilon_{0}}= 9 \times10^{9} SI unit]

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  4. Question 4

    20 Apr 2026 S2

    126
    A charge QQ is placed at each corner of a cube of side rr. The potential at the centre of the cube is (ϵ0\epsilon_0 = permittivity of free space)

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