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Two identical conducting spheres A and B, each of radius R, carry equal charges and are separated by a large distance d (d >> R), exerting a force f0 on each other. A neutral conducting sphere of radius 2R is first touched to sphere A, then touched to sphere B, and finally removed far away. What is the new electrostatic force between A and B?

1. f0/4
2. f0/9
3. 5*f0/27
4. 4*f0/27

Correct answer: 5*f0/27

Solution

After the first touch, A loses 2/3 of its charge to the neutral sphere. After the second touch, B gains charge and retains only 1/3 of the combined total. The product of final charges on A and B is 5/27 times the original q², giving force 5f0/27.

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