Final answer:
The strength of the electric field as a line charge becomes infinitely long is determined by the charge distribution along the line, typically remaining constant at a given distance for a uniform charge distribution.
Step-by-step explanation:
When considering the behavior of electric field lines as a line charge becomes infinitely long, it is crucial to understand the properties of electric field lines. The strength of the electric field is based on the closeness of the field lines, which is quantifiable as the number of lines per unit area perpendicular to the lines. As a line charge becomes infinitely long, its influence extends to infinity, and the electric field strength due to that line of charge at a finite distance does not become zero or infinity. Instead, the electric field strength would be determined based on the charge distribution along the line. If the charge is uniformly distributed, the field at a given distance will remain constant and will not depend on the length of the charge distribution as it approaches infinity.