Question

I'm studying a problem involving the scattering of two charged particles, A and B, with a mass ratio of 1:4 and identical charges. The particles move towards each other with equal and opposite velocities.

I'm trying to understand their motion at the point of nearest approach. Specifically, I'm confused about whether the particles would momentarily stop and reverse directions or move with the same velocity toward one of the initial positions, specifically the initial position of the lighter particle.

Could someone help clarify the underlying physics that dictates the behavior of such a system? Does the Coulomb interaction affect the conservation of momentum? I think not because it's an internal force in this case.

Answer 1

The charged particles A and B, with a mass ratio of 1:4 and identical charges, will not momentarily stop and reverse directions at the point of nearest approach. Instead, they will continue to move with the same velocity toward one of the initial positions, specifically the initial position of the lighter particle.

Step-by-step explanation:

In a system involving the scattering of two charged particles, the behavior at the point of nearest approach is influenced by the interplay of kinetic and potential energies. The Coulomb interaction between the particles introduces a potential energy term into the system. However, this potential energy doesn't affect the conservation of momentum directly, as it is an internal force.

At the point of nearest approach, the kinetic energy of the system is at its minimum, and the potential energy is at its maximum. The particles, driven by their initial velocities, will continue to move, and the potential energy will be converted back into kinetic energy as they move away from each other.

The conservation of momentum is not violated because the Coulomb interaction is an internal force. Momentum is still conserved in the system overall. The particles' trajectory is determined by the interplay between kinetic and potential energies, and they will not come to a complete stop or reverse direction at the point of nearest approach.

Instead, they will continue their motion, reflecting the dynamic nature of the system. The specific behavior can be further analyzed by considering the potential energy function and solving for the trajectories using relevant equations of motion.