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Question

Three charges \( +3 \, \mu\text{C}, +3 \, \mu\text{C}, -6 \, \mu\text{C} \) are at the vertices of an
equilateral triangle of side 2 m. What is the force on \( -6 \, \mu\text{C} \)?

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Explanation

**Superposition principle** asserts net Coulomb force on charge equals vector sum of forces from each other charge independently, F_net = Σ F_i, where F_i = k q q_i/r_i² r̂_i. In equilateral triangle or square symmetry, components may cancel at centroid, producing equilibrium. F₁ = F₂ = 9 × 10⁹ × (3 × 6 × 10⁻¹²/(2)²) = 0.0405 N (attractive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.0405² + 0.0405² + 0.0016425) = 0.0702 N . Substituting values gives 0.07 N, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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