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Two identical balls, each of mass m = 0.9 g, carry equal charges, are joined by a thread, and are suspended from the ceiling (one above the other so that the two threads and the line joining the balls are collinear/vertical). Find the charge (in microcoulomb) each ball must carry so that the tension is the same in both threads. The centre-to-centre distance between the balls is R = 3 m.

1. q = 0.95 microC
2. q = 1.9 microC
3. q = 0.45 microC
4. q = 3.0 microC

Correct answer: q = 3.0 microC

Solution

Equal tension in the two collinear threads requires the Coulomb repulsion between the balls to equal the weight of one ball: k*q²/R² = m*g. Solving, q = R*sqrt(m*g/k). With m = 0.9 g = 0.9e-3 kg, g = 9.8 m/s², R = 3 m, k = 9e9: q = 3*sqrt((0.9e-3*9.8)/(9e9)) = 3*sqrt(8.82e-3/9e9) = 3*sqrt(9.8e-13) = 3*9.9e-7 = 2.97e-6 C, approximately 3.0 microC.

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