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Charge and surface charge density on spheres at the same potential (touched or connected)

This type of question, asked 6 times: 4 May 2023 S1, 11 May 2024 S2, 11 Apr 2026 S1, 13 Apr 2026 S2, 15 May 2026 S1, 19 May 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    4 May 2023 S1

    49
    A metallic sphere A isolated from ground is charged to +50 μC+50\,\mu\text{C}. This sphere is brought in contact with other isolated metallic sphere B of half the radius of sphere A. Then the charge on the two isolated spheres A and B are in the ratio

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  2. Question 2

    11 May 2024 S2

    40
    Two spherical conductors of capacities 3 μF3\,\mu\text{F} and 2 μF2\,\mu\text{F} are charged to same potential having radii 3 cm and 2 cm respectively. If 'σ1\sigma_1' and 'σ2\sigma_2' represent surface density of charge on respective conductors then σ1σ2\frac{\sigma_1}{\sigma_2} is

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  3. Question 3

    11 Apr 2026 S1

    124
    Two metal sphere of radius RR and 3R3R have same surface charge density σ\sigma. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1\sigma_1 and σ2\sigma_2, respectively. The ratio σ1σ2\dfrac{\sigma_1}{\sigma_2} is.

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  4. Question 4

    13 Apr 2026 S2

    128
    Two isolated metallic spheres of radii RR and 2R2R are charged such that both have the same charge density σ\sigma. The spheres are then connected by a thin conducting wire. If the new charge density of the larger sphere is σ1\sigma_1. The ratio σ1\sigma_1 to σ\sigma is

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  5. Question 5

    15 May 2026 S1

    124
    A large insulated sphere of radius rr, charged with QQ C is placed in contact with a small insulated uncharged sphere of radius r1r_1 and is then separated. The charge on the smaller sphere will now be

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  6. Question 6

    19 May 2026 S2

    126
    Two spheres A and B of radius aa and bb respectively are at the same electric potential. The ratio of the surface charge densities of A to that of B is

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