Final distance between two charges, identical particles approaching each other

In summary, two charged, identical particles with a mass of 4.5 mg and a charge of 30 nC each are moving towards each other with equal speeds of 4.0 m/s. When the distance between them is 65 cm, they will be closest to each other. To calculate the final distance (rf), we can use the conservation of energy equation and the potential energy equation for a system of two charges. However, it is important to make sure the correct units are used, including the factor of 4Pi and the electric permittivity.
  • #1
Alfaraj
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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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  • #2
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.
 

FAQ: Final distance between two charges, identical particles approaching each other

1. What is the equation for calculating the final distance between two charges?

The equation for calculating the final distance between two charges is given by Coulomb's law, which states that the force of attraction or repulsion between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

2. How do identical particles approaching each other affect the final distance between them?

Identical particles approaching each other will have no effect on the final distance between them, as the distance is solely determined by the magnitude and sign of their charges.

3. Can the final distance between two charges ever be zero?

Yes, the final distance between two charges can be zero if the two charges are of opposite sign and have equal magnitudes. In this case, the forces cancel each other out and the charges will be at rest at a distance of zero from each other.

4. How does the final distance between two charges change if the charges have different magnitudes?

The final distance between two charges will decrease as the magnitude of the charges increases, as the force between them will become stronger. The final distance will also be affected by the ratio of the magnitudes of the charges.

5. What is the significance of the final distance between two charges in practical applications?

The final distance between two charges is important in many practical applications, such as determining the strength of an electric field or the potential energy of a system. It also plays a crucial role in understanding the behavior of charged particles in fields and in the design of electronic devices.

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