Identical conducting spheres A and B, each carrying charge q, repel with force F. A third identical uncharged sphere C first touches A, then B, and is removed. Find the new repulsive force between A and B (their radii are negligible compared with separation).
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Question

Identical conducting spheres A and B, each carrying charge q, repel with force F. A third identical uncharged sphere C first touches A, then B, and is removed. Find the new repulsive force between A and B (their radii are negligible compared with separation).

Options

G1 Physics · Accepted Answer

Step 1: Initially qₐ = qᵦ = q, and F = kq²/r². Step 2: When C (uncharged) touches A, total q is shared equally: qₐ′ = q꜀′ = q/2. Step 3: Then C with q/2 touches B with q. Their combined charge is 3q/2, shared equally: qᵦ′ = q꜀″ = 3q/4. Step 4: A remains at q/2 after C departs. Step 5: New force F′ = k(q/2)(3q/4)/r² = (3/8)kq²/r² = 3F/8. Final answer: 3F/8, Option D.