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Question

An infinite line charge has \( \lambda = 5 \times 10^{-7} \, \text{C/m} \). What is the electric field
at 10 cm?

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Explanation

**Charge density formulation** allows integration over extended bodies, but highly symmetric cases yield simple expressions. Infinite line gives E ∝ λ/r, unlike point charge 1/r², reflecting different geometry of source. E = (2 k λ/r) . E = (2 × 9 × 10⁹ × 5 × 10⁻⁷/0.1) = 9 × 10⁴ N/C . Substituting values gives 9.0 × 10⁴ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency. This aligns with NCERT Class 11 treatment, emphasizing conservation, symmetry and dimensional consistency useful for CBSE, NEET and CUET.

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