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    Question

    Two identical spheres with charges +4q and –q are

    brought into contact and then separated. What is the final force between them if their centers are r meters apart?
    A k(9q²)/r² Correct Answer Incorrect Answer
    B k(1.5q)²/r² Correct Answer Incorrect Answer
    C k(1.5q)(–1.5q)/r² Correct Answer Incorrect Answer
    D k(2.5q)²/r² Correct Answer Incorrect Answer

    Solution

    Initial charges: ·         Sphere 1: +4q ·         Sphere 2: -q When identical conducting spheres are brought into contact: The total charge redistributes equally between the two spheres. Total charge calculation: Total charge = (+4q) + (-q) = +3q After contact and separation: Since the spheres are identical, the total charge splits equally: ·         Final charge on each sphere = (+3q)/2 = +1.5q So both spheres end up with charge +1.5q each. Using Coulomb's law: F = k|q₁q₂|/r² With both charges being +1.5q: F = k|(+1.5q)(+1.5q)|/r² F = k(1.5q)²/r² F = k(2.25q²)/r²

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