Some special cases for consideration of Electric Field lines.
1. For the case of two identical charges located on the X axis at +1m and -1m,
consider the field lines that go along the X axis from each charge toward the origin.
They simply disappear at the origin!
There are an infinite number of lines that can be drawn in the central Y-Z plane
from near the origin, outward, but no way to connect any one of them to one of the
lines on the X-axis.
2. Just beyond the charges, the field lines that move outward along the X-axis give
no indication of what they should do "at" infinity. Of course, there are no negative
charges in this space for any lines to "close" on. But since the field is going to be
zero "at" infinity, we really can't say what their behavior will be.
3. In short, field lines are a way to visualize the geometry of the electric field in a
limited region of space.