Electrostatic and gravitational forces

AI Thread Summary
To determine the distance between a single proton and a group of 13 protons where the electrostatic force equals the gravitational force on a proton, the relevant formulas involve the mass of a proton and its charge. The mass of a proton is 1.67 x 10^-27 kg, and its charge is 1.6 x 10^-19 C. The electrostatic force can be calculated using Coulomb's law, while the gravitational force can be derived from the mass and gravitational acceleration. The user attempted to calculate the distance using the formula but expressed confusion about incorporating the group of 13 protons. Ultimately, the calculated distance of 43.7 centimeters was questioned for accuracy.
Rowie25
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Homework Statement


How far (in cm) apart must be proton from group of 13 protons if the magnitude of the electrostatic force acting on either one due to the others is equal to the magnitude of the gravitational force on a proton at Earth's surface?


So, I know that the mass of a proton is 1.67*10^-27 kg and that the charge on the proton is 1.6*10^-19 C. I am using the formula: 1/(4piEo) times (q1q2 divided by r^2) equals mg. So I thought you could set it up like this: (1.6*10^-19 times (13)(1.6*10^-19) divided by (1.6*10^-27)(9.8). That multiply that quotient by r^2=9*10^9. I don't think I did it right, I'm confused at what to do with the 13. Thanks!
 
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I got something like .437 meters and changed that into 43.7 centimeters. Does that seem right?
 

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