Practice question
Question
Three charges \( +7 \, \mu\text{C}, -5 \, \mu\text{C}, +3 \, \mu\text{C} \) are at the vertices of an
equilateral triangle of side 2 m. What is the force magnitude on \( +7 \, \mu\text{C} \)?
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 = 9 × 10⁹ × (7 × 5 × 10⁻¹²/(2)²) = 0.07875 N (attractive). F₂ = 9 × 10⁹ × (7 × 3 × 10⁻¹²/(2)²) = 0.04725 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.07875² + 0.04725² + 0.00372) = 0.098 N . Substituting values gives 0.098 N, which matches expected magnitude
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