Final distance between two charges, identical particles approaching each other

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SUMMARY

The final distance between two identical charged particles, each with a mass of 4.5 mg and a charge of 30 nC, moving towards each other at 4.0 m/s, can be calculated using the conservation of energy principle. The relevant equations include the conservation of energy (Ki + Ui = Kf + Uf) and the potential energy formula (U = (q1 * q2)/r12). The correct approach involves ensuring proper unit conversion and accounting for the electric permittivity constant in SI units. The final distance when the particles are closest to each other is determined by solving for rf in the energy equation.

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  • Knowledge of unit conversion in SI units
  • Basic grasp of electrostatics and Coulomb's law
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  • Learn about the role of electric permittivity in calculations involving charges
  • Practice solving problems involving two-body interactions in physics
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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.
 
Last edited:
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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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