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Question

Three charges \( +4 \, \mu\text{C}, -4 \, \mu\text{C}, +2 \, \mu\text{C} \) are at the vertices of an
equilateral triangle of side 1 m. What is the force magnitude on \( +4 \, \mu\text{C} \)?

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Explanation

**Independent action of charges** allows total force or field as vector sum. Geometry dictates distances to evaluation point, and resultant follows Σ k q_i/r_i², explaining zero field at symmetric centres for equal charges. F₁ = 9 × 10⁹ × (4 × 4 × 10⁻¹²/1) = 0.144 N (attractive). F₂ = 9 × 10⁹ × (4 × 2 × 10⁻¹²/1) = 0.072 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.144² + 0.072² + 0.010368) = 0.187 N . Substituting values gives 0.187 N, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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