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I understand that both the electric and gravitational forces are inversely proportional to the squared distance from the point source and that the gravitational constant is around $10^{-20}$ times Coulomb's constant.

I don't understand why this suffices to conclude that the gravitational force is stronger than the electric force. The two constants that I see getting compared here have different units. One involves electric charges, while the other involves gravitational masses. To me, this makes as much sense as saying that a second is larger than a meter.

Is it related to the energy densities of these fields? If yes, how? I think that it is not the duplicate of the mentioned question because the point being asked in that question is why do we consider gravitational fields weaker even if they are more dominant in the universe at macroscopic levels. But, I want to ask that what are the criteria based on which we define the relative strength or weakness of forces/fields. What do we exactly mean by declaring a force/field stronger than the other? Is it related to their energy densities?

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You're just comparing forces to forces, Newtons to Newtons. I guess if you want to be really nitpicky, you're talking about force per charge vs force per mass. But when one says that the electric force is much stronger than the gravitational force, one means that in dealing with the usual objects, like electron, the effects of gravity on the electron's motion are negligible when compared to the effects of the electromagnetic forces - negligible by many orders of magnitude.

Melativity
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