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I agree that its a bit of a stretch to assert that this is a "universal" property of fields. But I think that it can be construed in much the same sense as is "potential theory," where we posit mathematical interactions of the gravitational and electric sort and abstract from them a generic theory that applies to any field that obeys certain properties, such as gravity or electricity, where only the values of the constants change, depending on which one you are talking about.
Then consider the magnetic interaction. How do you fit the velocity
dependence on the "field susceptible property" (- i.e., the moving charge}
into this algorithm?