Two identical positive charges q are placed in a smooth horizontal circular groove at points separated by 90° at the centre. A third positive charge is placed in the groove so that all three charges are in tangential equilibrium immediately after release. The third charge must be placed:
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Question

Two identical positive charges q are placed in a smooth horizontal circular groove at points separated by 90° at the centre. A third positive charge is placed in the groove so that all three charges are in tangential equilibrium immediately after release. The third charge must be placed:

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G1 Physics · Accepted Answer

For a positive third charge, symmetry places it on the diameter opposite the midpoint of the 90° minor arc, i.e. at 225° if the original charges are at 0° and 90°. Tangential equilibrium gives Q/q = (2+√2)³ᐟ² / 2 ≈ 3.154. Therefore, Q = [(2+√2)³ᐟ²/2]q.