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Question

Three equal charges \( q = 3 \, \mu\text{C} \) are at the vertices of an equilateral triangle of side 1
m. What is the electric field at the centroid?

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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. Distance from vertex to centroid: r = (l/√(3)) = (1/√(3)) m . E = (k q/r²) = 9 × 10⁹ × (3 × 10⁻⁶/(1/√(3))²) = 81 × 10⁴ N/C per charge. By symmetry (all +q ), vectors cancel, so Eₙₑt = 0 . Substituting values gives 0 N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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