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Two spheres, each carrying a charge q, hang from the same point of suspension by threads of length 2 m, in a space free from gravity. The distance between them will be

Asked in GSEB Board July 2017 · Equilibrium and small oscillations

Answer: (3) 4.0 m

Step-by-step solution

Given: thread length L=2 m; like charges q on both spheres; no gravity.

Idea: with no weight, the only forces on each sphere are the Coulomb repulsion from the other sphere and the tension in its thread.

The repulsion acts along the line joining the spheres. Equilibrium needs the tension to be exactly opposite to it, which happens only when the thread lies along that same line.

At any smaller angle the repulsion has a part across the thread that nothing balances, so the spheres keep swinging apart until the threads are in one straight line through the support.

Distance =L+L=2L=2×2=4.0 m.

Why the other options are wrong

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