Final answer:
The linear charge density is calculated using the electric field formula E = λ/(2πε₀r) for an infinite line charge and substituting the electric field and the distance from the charge into this formula.
Step-by-step explanation:
The student has asked about determining the linear charge density given that an infinite line charge produces an electric field of 18×10⁴ N/C at a distance of 4 cm. In physics, specifically electromagnetism, the electric field (E) due to an infinitely long straight wire with uniform linear charge density (λ) can be found using the formula E = λ/(2πε₀r), where ε₀ is the vacuum permittivity and r is the distance from the line charge. By rearranging the formula and solving for λ, we get λ = E × 2πε₀r. Substituting the given values (E = 18×10⁴ N/C and r = 4×10⁻₂ m), and using ε₀ = 8.854×10⁻¹² C²/(N·m²), we can calculate the linear charge density.