Two identical small conducting spheres carry positive charges q₁ and q₂ and are separated by distance d. The electrostatic force between them is F. They are brought into contact, then separated again to the same distance d. If the new force is F′, which statement is necessarily correct?
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Question

Two identical small conducting spheres carry positive charges q₁ and q₂ and are separated by distance d. The electrostatic force between them is F. They are brought into contact, then separated again to the same distance d. If the new force is F′, which statement is necessarily correct?

Options

G1 Physics · Accepted Answer

Initially, F = kq₁q₂/d². After contact, identical spheres share charge equally, so each has (q₁+q₂)/2. Therefore F′ = k(q₁+q₂)²/(4d²), and F′/F=(q₁+q₂)²/(4q₁q₂). Since (q₁-q₂)²≥0, (q₁+q₂)²≥4q₁q₂. Hence F′≥F, with equality only when q₁=q₂.