The problem is a conflict between two conventions (1) that traces field lines between electric charges so that the tangent to a field line at a particular point indicates the direction of the field at that point, and (2) that the areal density of field lines (in three dimensions) is indicative of the field strength.
There is no conflict in the case of cylindrical symmetry, but as already pointed out, representing a slice through a 3-D field pattern can produce a conflict.
In Volume II section 1-2 of the Feynman Lectures on Physics, Feynman
gives a couple of different schemes for representing a vector field
graphically. In figure 1-2 he provides an example of a vector field
diagram in which he shows field lines starting up in empty space (other
than at the edges of the diagram). He says that ..."it will require, in
general, that new lines sometimes start up in order to keep the number
up to the strength of the field." It is my understanding, in terms of
the electric field, that new lines should start up only at positively
charged particles/objects and/or at infinity. Has the convention
changed since the Feynman Lectures came out? Of those of you that teach
students how to draw and/or interpret vector field diagrams that use
field lines, do any of you adhere to the convention that field lines
begin at empty points in space "in order to keep the number up to the
strength of the field." ?
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