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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?

Asked in Odisha NEET 2019 · Redistribution of charge

• (1) σ₁=5/6σ, σ₂=5/2σ
• (2) σ₁=5/2σ, σ₂=5/6σ
• (3) σ₁=5/2σ, σ₂=5/3σ
• (4) σ₁=5/3σ, σ₂=5/6σ

Step-by-step solution

Why the other options are wrong

• (1) Gives the smaller sphere the smaller density, the opposite of σ∝1/R at equal potential; the pair also fails charge conservation (it totals (130)/3πσ R², not 20πσ R²).
• (2) σ₁=5/2σ is what the small sphere gets if the charge is split equally (10πσ R² each). Contact equalises potential, not charge, and with σ₂=5/6σ the total charge is not conserved.
• (3) σ₁=5/2σ matches an equal split of charge, but σ₂=5/3σ does not follow from that or any other single slip; the pair fails charge conservation.

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