Scattering of two charged particles

In summary, the problem involves two identical charged particles of mass m and charge e, initially far apart. One particle is stationary at the origin while the other approaches it with velocity v along a line x=b, y=0, where b is equal to e^2/2pi*epsilon_0*mv^2. The task is to find the scattering angle in the center of mass frame and the directions in which the two particles emerge in the laboratory frame. The relevant equation for this problem is the Rutherford scattering equation. The attempt at a solution involves considering the particle's initial trajectory as a straight line with impact parameter b.
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Dazed&Confused
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Homework Statement


Two identical charged particles, each of mass [itex]m[/itex] and charge [itex]e[/itex], are intitialy far apart. One of the particles is at rest at the origin, and the other approaching it with velocity [itex]v[/itex] along the line [itex]x=b, y=0[/itex] where [itex] b=e^2/2 \pi \epsilon_0 mv^2[/itex]. Find the scattering angle in the CM frame, and the directions in which the two particles emerge in the Lab.

It then quotes a relevant section which was on Rutherford Scattering

Homework Equations

The Attempt at a Solution


Calling [itex]x=b, y=0[/itex] a line threw me off. I'm not sure what they mean by that.
 
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  • #2
Dazed&Confused said:
Calling [itex]x=b, y=0[/itex] a line threw me off. I'm not sure what they mean by that.
I'm not sure either. Maybe they mean that the particle is initially traveling in the x-z plane along a line that is parallel to the z axis at x = b.
 
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Likes SammyS
  • #3
That does make sense, although why introduce a third dimension if the particles are in a plane? Anyway I'll try it with what you say.
 
  • #4
Dazed&Confused said:
That does make sense, although why introduce a third dimension if the particles are in a plane?

Good point.

The important thing is that the projectile particle is initially moving along a straight line with impact parameter b. I think that's all you really need to know.
 

1. What is the scattering of two charged particles?

The scattering of two charged particles is a phenomenon that occurs when two particles with electric charge interact with each other. This interaction can cause changes in the paths and velocities of the particles, and can result in the transfer of energy between them.

2. What factors affect the scattering of two charged particles?

There are several factors that can affect the scattering of two charged particles, including the strength of the electric charge, the distance between the particles, and the masses of the particles. These factors can determine the strength and direction of the interaction between the particles.

3. How is the scattering of two charged particles studied?

The scattering of two charged particles is studied through experiments and mathematical models. Scientists use particle accelerators to create controlled collisions between particles and observe the resulting scattering patterns. They also use mathematical equations, such as the Coulomb's law and the Lorentz force law, to predict and analyze the behavior of the particles.

4. What is the significance of studying the scattering of two charged particles?

Studying the scattering of two charged particles allows scientists to understand the fundamental forces and interactions at the subatomic level. This knowledge is crucial for advancements in fields such as particle physics, materials science, and nuclear energy. It also helps us to better understand and control natural phenomena, such as lightning and the behavior of stars.

5. Can the scattering of two charged particles be controlled or manipulated?

Yes, the scattering of two charged particles can be controlled and manipulated through the use of external electric and magnetic fields. Scientists can also manipulate the physical properties of the particles, such as their mass and charge, to alter their scattering behavior. This has important applications in fields such as particle accelerators and medical imaging techniques.

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