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

Answer: (b). Charges: q₁ = 4π R²σ, q₂ = 16π R²σ; total 20π R²σ. Connected ⇒ q ∝ r: q₂' = 2/3× 20π R²σ = 40/3π R²σ. σ' = (q₂')/(4π(2R)²) = 5/6σ So the answer is (b) 5/6.

Two isolated metallic solid spheres of radii R and 2R are charged… | JEE Main 2023 (30 Jan, Shift 1)

Q66JEE Main 2023 · 30 JAN · SHIFT 1Medium

Electric Potential & Equipotentials

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

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Answer: (b)

Charges: $q_1 = 4\pi R^2\sigma$ , $q_2 = 16\pi R^2\sigma$ ; total $20\pi R^2\sigma$ .
Connected $\Rightarrow q \propto r$ : $q_2' = \frac{2}{3}\times 20\pi R^2\sigma = \frac{40}{3}\pi R^2\sigma$ .
$\sigma' = \frac{q_2'}{4\pi(2R)^2} = \frac{5}{6}\sigma$
So the answer is (b) $\frac{5}{6}$ .

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Electric Potential & Equipotentials question from JEE Main 2023 (30 Jan, Shift 1)

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