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Question

A point charge \( -8 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a
point 4 m along the z-axis?

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Explanation

**Fundamental property of charge** includes additivity and quantization, meaning net charge equals algebraic sum of constituents and each is multiple of e. When rod loses charge, electron removal is inferred, and n = q/e gives transferred count. E = (k |q|/r²) . k = 9 × 10⁹ N·m²/C² , q = 8 × 10⁻⁶ C , r = 4 m . E = 9 × 10⁹ × (8 × 10⁻⁶/(4)²) = 9 × 10⁹ × (8 × 10⁻⁶/16) = 4.5 × 10³ N/C . Substituting values gives 4.5 × 10³ 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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