Long range forces?

Question

A force/field which depends inversely on the square of the distance of the source from the point of interest (like electric field depends on $1/r²$, where $r$ is the distance between the the source charge and the test charge) is said to be 'long range'. Why?

Answer 1

Actually there is a well accepted sense of what long range means. You do have to be careful with different contexts.

In Quantum Field Theory (QFT) and classical FT the field related to a classical force that goes as $1/r^2$ can be radiative, with its amplitude going as 1/r in the far field (i.e., long range). It means that the amplitude of the field that causes that force can propagate and be 'felt' at great distances. The perfect example is electromagnetic forces, and the electromagnetic field. We are able to detect the electromagnetic field emitted billions of light years away. In General Relativity a propagating gravitational field (manifested as spacetime curvature and equivalent to a gravitational force in the weak field limit), also has its amplitude go as 1/r far enough away, and we can detect it also far away. We detected gravitational waves from black holes a billion or so light years away.

In contrast, nuclear forces, or more basically the strong and weak force, have a field that goes down much faster than 1/r, and are almost undetectable outside the nucleus. A mile away you cannot detect it (but an explosion in an A bomb in a very local area can cause heat and radiation (electromagnetic, as well as particles) to go out for miles. Or, from the Sun, across the solar system. Still, those are NOT nuclear or stron or weak waves, rather electromagnetic and particles that were shot out.).

The basic reason from FT or QFT and equivalent theory is that long range forces or fields are carried by zero mass particles, such as the photon or graviton. Massive force fields like the strong and weak FIELDS decay proportionally to exp(-$kmr$)/r, i.e., negative exponentially in r as well for m not equal to zero. This general behavior can be deduced for QFT and is a good first generic approximation for non-zero mass fields, for a scalar field, as one obtains from a Yukawa potential. The spin 1 and 2 electromagnetic and gravitational fields are more complex but the idea holds as to what would happen if they were massive. The strong and weak fields are even more complex, but this is the basic simplest way of looking at why those other fileds, other than electromagnetic and gravitational, are short range.

There are also non-elementary contact forces like friction, clearly derived from molecular forces, and which are also short range, due to a complex balancing of electromagnetic forces in atoms and molecules. The basic physics forces from which all else are derived are the ones discussed in the paragraphs above

Answer 2

This source defines short-range forces as:

Non-bonded interactions can be divided into two classes; short and long range interactions. Formally a force is defined to be short ranged if it decreases with distance quicker than $r^{-d}$ where $d$ is the dimensionality of the system (usually 3).

And the opposite would then be long-range forces and the answer to your question. I'm not sure how official this definition is, but it is a good pointer.

Usually we talk about contact forces (see here and here). They would be the bonded forces that the above quote mentions, and I believe that the short-range forces normally are placed within this category as well - they only act at so close range that it could basicly be defined as contact.

Answer 3

The term long range force means that at infinite distance the force never actually becomes zero.

These forces do not require any physical contact to exist. Forces like normal force, frictional force need contact in order to exist but forces like gravitational force and electrostatic force do not need any physical contact to come into existence.