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Two conducting spheres joined by a wire: ratio of charges, charge densities or surface fields

This type of question, asked 4 times: 26 Jul 2022, 30 Jan 2023, 8 Apr 2024, 2 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    26 Jul 2022

    95
    Two uniformly charged spherical conductors A and BB of radii 5 mm5\text{ }mm and 10 mm10\text{ }mm are separated by a large distance. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere AA and BB will be:

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  2. Question 2

    30 Jan 2023

    3
    Two isolated metallic solid spheres of radii RR and 2R2R are charged such that both have same charge density σ\sigma. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is σ′\sigma^{'}. The ratio σ′σ\frac{\sigma^{'}}{\sigma} is:

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  3. Question 3

    8 Apr 2024

    15
    Two charged conducting spheres of radii a and bb are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

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  4. Question 4

    2 Apr 2026 S1

    9
    Two charged conducting spheres S1S_{1} and S2S_{2} of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1S_{1} and S2S_{2} spheres are ES1E_{S1} and ES2E_{S2} respectively. The value of ES1ES2\frac{E_{S1}}{E_{S2}} is ____\_\_\_\_ .

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