Let's imagine I have 2 spheres made out of metal, each with a mass of exactly 1 kg. These spheres are sitting in a place in the universe devoid of any significant masses - meaning there is negligible gravitational force on my beautiful spheres.
I give each sphere a charge of 1/100000th of a Coulomb and move their centers of mass exactly 1 meter away from each other. Then I release them.
By Coulomb's law, they begin to accelerate away from each other, and the force on each one is given by:
I iterated through this calculation in Excel 10,000 times at 1/100th of a second intervals, and came up with an acceleration at t=100s of 2.55*10^-5 m/s^2, and the spheres ended at 187.77 meters away from each other.
My question is, will my beautiful spheres ever reach an essentially constant velocity?
I've tried to approach this theoretically - integrating acceleration with respect to time from t=0 to t=infinity should tell me whether or not there is a finite ending velocity. However, one value for acceleration depends on previous values, so I am not sure where to go.
So, at the end of time, will my spheres be moving at a finite velocity or will they be moving away from each other infinitely fast?