As I recall from my undergraduate physics a long time ago, "field" was
defined as "force per UNIT (mass/charge/hadron number, etc. -- take your
pick)", just as "potential" was "potential energy per UNIT (whatever)."
The field is then the gradient of the potential (if the potential can be
defined at all); the force is the gradient of the potential energy. In
thermodynamic terms, force is an extensive variable; field is an intensive
variable.
As to relative strengths of the forces, gravity and E&M can be "compared"
by computing the gravitational force and the electrostatic force between,
say, an electron and a proton at a given distance apart (say, the Bohr
radius of the hydrogen atom). Since both forces scale the SAME WAY with
distance, this is a reasonable way to make a comparison -- except it
muddies the issue of whether it's the FORCES that are radically different
strengths or that the CHARGES/MASSES are not "equivalent." Nonetheless,
the ratio of the grav. & E&M forces in the hydrogen atom is illustratively
useful.
As to comparisons of these two inverse-square-law forces with the other
two, the comparison gets murkier. For the strong nuclear force, it's
probably reasonable to ask what the strong force between two protons IN A
NUCLEUS is compared to the electrostatic repulsion between them. How one
does this for the weak nuclear force (which governs beta-decay) I truly
don't see -- is it perhaps by comparison of energy density in the fields?
Peter Vajk
St. Joseph Notre Dame High School
Alameda, CA