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Question

A conducting sphere of radius 19 cm has an electric field of \( 3 \times 10^3 \, \text{N/C} \) at 38 cm
from its center. What is the charge?

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Explanation

**Inverse-square law** for charges states F ∝ 1/r² while increasing with charge product. Using k = 9×10⁹ N·m²/C², force at distance r follows F = k q₁q₂/r², forming basis for pairwise force calculation. E = (k q/r²) . 3 × 10³ = 9 × 10⁹ × (q/(0.38)²) . q = (3 × 10³ × 0.1444/9 × 10⁹) = 4.81 × 10⁻⁸ C . Substituting values gives 4.81 × 10⁻⁸ C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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