 Quote by clallier
How much stronger is the strong nuclear force compared it to the electromagnetic force beyond what could be accounted for by the inverse of the distance squared?
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Welcome to PhysicsForums, clallier!
It is a bit difficult to answer your question since these 2 forces do not operate using the same mechanism. The strongest component of the strong force would be considered quark confinement, which does not actually operate on the basis of inverse distance squared. Instead, it gets stronger to a point as distance increases (and we are talking very small distances, the size of a proton/neutron). This is many orders of magnitude stronger than the electromagnetic force, so much so that the EM force is negligible at this range.
The other well-known component of the strong force is nuclear binding, which is what keeps the positive charges in the nucleus together despite their electromagnetic repulsion. At the range of the nucleus, the strong force is perhaps 2 or 3 orders of magnitude stronger than the EM force although again, they are not directly comparable.
See this for some more detail information:
http://en.wikipedia.org/wiki/Strong_interaction