LinesofForce diagrams work for "inverse square Force Laws", but not all force laws are of that type.
What are Force Laws?
Force laws are formulae for reckoning the force between two objects. Familiar examples are:
from steady wind
approx. chemical bond
magnetic poles
gravity
Note that the most fundamental forces are "inverse square".
Think carefully about graphical representations of these forces and the corresponding energies,
remembering that F = dE / dr:

