Lines-of-Force diagrams work for "inverse square Force Laws".

What are Force Laws?

Force laws are formulae for reckoning the force between two objects. Familiar examples are:

Law	r (Distance) Dependance	Examples
[constant force]	F = const	force on a plow
Hooke's Law	F = const * r	ideal spring approx. chemical bond
Coulomb's Law	F = const / r2 "inverse square"	electrical charges magnetic poles gravity

Note that the most fundamental forces are "inverse square".

Think carefully about graphical representations of these forces and the corresponding energies: