Question

What is the difference between contact forces and field forces.

Answer 1

Contact forces are forces that require the actual contact (touching) of two pieces of matter.  There are a variety of contact forces.  A very common one is friction.  Anytime that two surfaces are in contact with one another, there is friction between the two surfaces.  The surfaces don't have to be solid either.  A skydiver still experiences friction as he "slides" through the air.  Specifically that is fluid friction.  Other types of contact forces are elastic, spring, and tension forces.  

A field force is a force that works at a distance.  No touching is required.  Gravity is a good example of a field force, because it works whether or not an object is touching something or touching nothing at all.  Two other forces of this type are electrical force and magnetic force. 

Answer 2

A "contact" force is effectively zero at large distances. 
At some distance of separation the force rises rapidly from zero with even a small decrease in the separation R. 
In a "perfect" surface the force would rise to infinity ie the surface could not flex or compress in any way. 


A field involves some form of FLUX which is shared over an area about its source. 
The geometry of the situation determines the area that the flux is shared over but the strength of the field is always inversely proportional to the area that the field is shared over. 
For example a point source has an area 4 pi() r^2 
so the field has a strength proportional to 1/ r^2