# The effect of a stationary proton on a stationary electron

1. The problem statement, all variables and given/known data
On the utterly unrealistic assumption that there are no other charged particles in the vicinity, at what distance below a proton would the upward force on an electron equal the electrons weight?

2. Relevant equations
I used Newtons universal law of gravitation as well as Coulombs law.

3. The attempt at a solution
Basically, I equated the sum of the forces on the electron (due to the proton) to the weight of the electron. The sum of the aforementioned forces correspond to the gravitational attractive force and the electrical attractive force (both forces being produced by the proton).

I got an answer of 4.85 meters. Right or wrong, I don’t really care because the number will be wrong by virtue of entering the values into the calculator wrong (hopefully); I’m definitely comfortable with the methodology. My problem is the language in this exercise. The weight of the electron depends on the acceleration due to gravity (which, on earth, is 9.8 m/s^2) of some other mass.

I arrived at 4.85 meters by assuming that this experiment takes place on earth. I’m not comfortable with making that assumption, but I’m also not comfortable with having to calculate the acceleration of a mass that is in the presence of a proton (the mass, for this example, would be the electron). I feel like calculating such a quantity would be out of the scope and spirit of the problem.

In a nutshell, my question pertains to the intent of the word ‘weight’. Do I calculate ‘g’ for an object in the presence of its gravitational field or do I assume this experiment takes place on earth?

Any guidance on this would be much appreciated. Thank you.

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