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Two identical metallic spheres A and B placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

1. 3F/2
2. 3F/4
3. 3F
4. 2F

Correct answer: 3F/4

Solution

C (uncharged) touching A gives each q/2; C then touching B gives both 3q/4. At the midpoint (r/2 from each), force from B = k(3q/4)(3q/4)/(r/2)^2 = (9/4)F and from A = (3/2)F act oppositely, so net force on C = (9/4 - 3/2)F = 3F/4, option (3F/4).

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