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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?

1. σ₁ = 5σ/3, σ₂ = 5σ/6
2. σ₁ = 5σ/6, σ₂ = 5σ/2
3. σ₁ = 5σ/2, σ₂ = 5σ/6
4. σ₁ = 5σ/2, σ₂ = 5σ/3

Correct answer: σ₁ = 5σ/3, σ₂ = 5σ/6

Solution

When the spheres are brought into contact, charge redistributes such that their potentials become equal. The charge on each sphere is proportional to its surface area. After separation, the surface charge density is calculated using the redistributed charge and the surface area of each sphere. The correct result is σ₁ = 5σ/3 and σ₂ = 5σ/6.

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