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Two isolated conducting spheres S1 and S2 have radii (2/3)R and (1/3)R and carry charges 12 uC and -3 uC respectively, far apart from each other. They are then joined by a conducting wire. A long time later, the charges on S1 and S2 are respectively:
- 6 uC and 3 uC
- +4.5 uC and -4.5 uC
- 3 uC and 6 uC
- 4.5 uC on both
Correct answer: 6 uC and 3 uC
Solution
Connected spheres reach equal potential, so charge distributes in proportion to radius: q1/q2 = r1/r2 = (2/3R)/(1/3R) = 2. Total charge = 12 - 3 = 9 uC. So q2 = 9/3 = 3 uC and q1 = 6 uC.
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