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Question

An infinite line charge has \( E = 6.3 \times 10^5 \, \text{N/C} \) at 7 cm. What is \( \lambda \)?

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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 = (2 k λ/r) . 6.3 × 10⁵ = (2 × 9 × 10⁹ × λ/0.07) . λ = (6.3 × 10⁵ × 0.07/18 × 10⁹) = 2.45 × 10⁻⁶ C/m . Substituting values gives 2.45 × 10⁻⁶ C/m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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