How Would Quantum Forces Change If the Classical Charge Equation Altered?

[kurious]

If the classical attraction between two coulomb charges was
constant x q1 x q2 / r ^3 or another constant x q1 x q2/ r^4 instead of
k x q1 x q2 / r ^2 (perhaps the constants could still be the
same-though I doubt it)
what would be the force relations on a quantum scale using coupling
constants?
Also what are the force relations if the r terms are on the top line
so force increases with distance?


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[ahrkron]

I don't quite understand what you are asking.
Maybe you can show which "normal" (i.e., with an inverse square law) version of "force relations on a quantum scale" you are thinking about, so that we can speculate on how they change if r^2 is replaced by r^3.

Also, it may help to know your motivation for this question.

 

[kurious]

If qft can derive kqq/r*r for large distances then at short distances shouldn't the force between charges be expressible in terms of a similar relation with different power of r and a different value of k.