Practice question
Question
An infinite line charge has \( \lambda = 3 \times 10^{-6} \, \text{C/m} \). What is the electric field
at 15 cm?
Explanation
**Quantization of charge** states observable charge is integer multiple of elementary charge e = 1.6×10⁻¹⁹ C, q = n·e, and total charge is conserved in isolated systems. Loss of electrons produces positive charge, and number of transferred electrons follows n = q/e, linking macroscopic charge measurement to microscopic carriers. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 3 × 10⁻⁶/0.15) = 3.6 × 10⁵ N/C . Substituting values gives 3.6 × 10⁵ 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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