Both electrons and protons have mass, so it is easy to conclude that they exert a gravitational pull on each other. But also, they are charged, so an electrical force is applied. Would we expect a "double dipping" reaction? Or does the K coulomb constant takes that in consideration?
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As far as I know, the smallest mass that was shown to have a gravitational attraction on another mass was 706 mg - and that was with a ridiculously careful experiment.
Coulomb attraction of a proton and electron is so many orders of magnitude greater (especially since the mass of the electron is so small) that there's no way it affects the measured force. Only with electrically neutral objects can you begin to measure the force of gravity.
The ratio of the two forces is of course simply given by
$$R = \frac{4\pi\epsilon_0 Gm_pm_e}{Q_p Q_e}$$
Wolfram alpha tells us the ratio is $-4\cdot 10^{-40}$.
That's a lot of orders of magnitude. Well outside the scope of any experiment I can think of.
Floris
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This question stems from a misunderstanding, that the coulomb force was determined by measuring the force attracting a positive and a negative charge in a vacuum or something, and attributing all of it to the electric force.
In reality, that's not how Coulomb's constant $k = \frac{1}{4\pi \epsilon_0}$ was determined. More importantly, coulomb's constant is so much stronger than the gravitational constant that it wouldn't have mattered if it was done that way.
It would be like trying to adjust the 'top speed' rating of a car for the gravitational force between the car and all the surrounding buildings when its top speed was tested.
Señor O
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