Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them? (a) σ₁ = 5/3σ, σ₂ = 5/6σ (b) σ₁ = 5/6σ, σ₂ = 5/2σ (c) σ₁ = 5/2σ, σ₂ = 5/6σ (d) σ₁ = 5/2σ, σ₂ = 5/3σ

Answer: (a). Initial charges: q₁ = 4π R²σ, q₂ = 4π(2R)²σ = 16π R²σ; total = 20π R²σ. After contact q ∝ radius, ratio 1: 2: q₁' = 20/3π R²σ, q₂' = 40/3π R²σ. σ₁ = (q₁')/(4π R²) = 5/3σ, σ₂ = (q₂')/(16π R²) = 5/6σ So the answer is (a).

Two metal spheres, one of radius R and the other of radius 2R… | NEET 2019

Q95NEET 2019Medium

Electric Potential & Equipotentials

Two metal spheres, one of radius $R$ and the other of radius $2R$ respectively have the same surface charge density $\sigma$ . They are brought in contact and separated. What will be the new surface charge densities on them?

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Answer: (a)

Initial charges: $q_1 = 4\pi R^2\sigma$ , $q_2 = 4\pi(2R)^2\sigma = 16\pi R^2\sigma$ ; total $= 20\pi R^2\sigma$ .
After contact $q \propto$ radius, ratio $1 : 2$ : $q_1' = \frac{20}{3}\pi R^2\sigma$ , $q_2' = \frac{40}{3}\pi R^2\sigma$ .
$\sigma_1 = \frac{q_1'}{4\pi R^2} = \frac{5}{3}\sigma$ , $\sigma_2 = \frac{q_2'}{16\pi R^2} = \frac{5}{6}\sigma$
So the answer is (a).

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