Two isolated metallic spheres of radii R and 2R are charged such that both have the same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density of the larger sphere is σ₁. The ratio σ₁ to σ is (a) 9: 4 (b) 4: 3 (c) 5: 3 (d) 5: 6

Answer: (d). Initial charges: Q₁ = 4π R²σ, Q₂ = 16π R²σ, total 20π R²σ. After connecting, charge divides in ratio of radii 1:2: Q₂' = 23×20π R²σ = 40/3π R²σ σ₁ = (Q₂')/(4π(2R)²) = (40)/(3×16)σ = 56σ So the answer is (d) 5:6.

Two isolated metallic spheres of radii R and 2R are charged such that… | MHT CET 2026 (13 Apr, Shift 2)

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Electric Potential & Equipotentials

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

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Answer: (d)

Initial charges: $Q_1 = 4\pi R^2\sigma$ , $Q_2 = 16\pi R^2\sigma$ , total $20\pi R^2\sigma$ .
After connecting, charge divides in ratio of radii $1:2$ : $Q_2' = \dfrac23\times20\pi R^2\sigma = \dfrac{40}{3}\pi R^2\sigma$
$\sigma_1 = \dfrac{Q_2'}{4\pi(2R)^2} = \dfrac{40}{3\times16}\sigma = \dfrac56\sigma$
So the answer is (d) $5:6$ .

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Electric Potential & Equipotentials question from MHT CET 2026 (13 Apr, Shift 2)

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