Final distance between two charges, identical particles approaching each other

AI Thread Summary
Two identical particles, each with a mass of 4.5 mg and a charge of 30 nC, are approaching each other at a speed of 4.0 m/s from an initial distance of 65 cm. The conservation of energy principle is applied, where the initial kinetic and potential energies are equated to the final energies. The potential energy formula used is U = (q1 * q2)/r12, but the user struggles to find the correct final distance between the charges. A suggestion is made to consider the correct units and include the factor of 4π and the electric permittivity in calculations. The discussion emphasizes the importance of proper unit conversion and energy conservation in solving the problem.
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Final distance between two charged, identical particles approaching each other

Homework Statement



Two identical particles, each with a mass of 4.5 mg and a charge of 30 nC, are moving directly toward each other with equal speeds of 4.0 m/s at an instant when the distance separating the two is equal to 65 cm. How far apart will they be when closest to one another? (Answer in cm.)


Homework Equations



Ki + Ui = Kf + Uf (Conservation of Energy)
U= (q1 * q2)/r12 (Potential energy of a system of two charges)

The Attempt at a Solution



I set the final kinetic energy of the system to be zero. In order to come up with an equation of the final distance (rf), I substituted the second equation into the first, and solved for rf. Unfortunately, I am still getting the wrong answer. Something is really missing in my approach to the problem.
 
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Your idea seems to be correct. Did you use the correct units?
Usually in SI-Units there will be an additional factor of 4Pi and the electrical permittivity in the electric potential.
 
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