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Two metallic spheres of radii R₁ and R₂ are charged. Now they are brought into contact with each other with a conducting wire and then separated. If the electric fields on their surfaces are E₁ and E₂ respectively, then (E₁)/(E₂) = ______.

Asked in GSEB Board July 2015 · Electrostatics of conductors

• (1) (R₂)/(R₁)
• (2) (R₁)/(R₂)
• (3) (R₂²)/(R₁²)
• (4) (R₁²)/(R₂²)

Step-by-step solution

Why the other options are wrong

• (2) This is the ratio of the charges, (Q₁)/(Q₂) = (R₁)/(R₂), not of the fields. The field also divides by R²: E = (kQ)/(R²).
• (3) This assumes the spheres end up with equal charges, so that E = (kQ)/(R²) gives (E₁)/(E₂) = (R₂²)/(R₁²). The wire does not share the charge equally; it makes the potentials equal.
• (4) No single slip gives (R₁²)/(R₂²); it is the equal-charge ratio (R₂²)/(R₁²) turned upside down. Sanity check: after sharing, E = V/R with the same V, so the smaller sphere has the stronger field, while (R₁²)/(R₂²) would give it the weaker one.

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