E and B fields for charged particle's parabolic motion

In summary, the conversation discusses the creation of a combination of electric and magnetic fields that can produce a similar effect to the (d) crests seen in a chain. The goal is to find a way to make a particle oscillate along a parabola and add a group velocity to the motion. The speaker also mentions their research on modeling self-replicating cracks using analog fields and the need for an analytical expression to achieve this.
  • #1
peasqueeze
7
2
I am looking to find a combination of electric and magnetic fields that create something similar to the (d) crests
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Currently, I have the cracks flipped clockwise 90deg, so that the crests are concave up. And each crest can be defined by a parabolic function (which are uniform with each new turn).

If I look at one crest, treat it as a particle moving in a concave up parabola I have...

$$\vec{E} = E\hat{y} , \vec{B} = B\hat{z}$$

Now, this is only for a single parabola. I need to make it so that the particle reaches a turning point and goes backwards along the same parabola (to the left now). I think this can be done by making B oscillate between a positive and negative value.

I also need to add a "group velocity" so that a string of these parabolas will create a chain like that seen in (d). In my example, though, the parabolas should be moving downwards.

TO SIMPLIFY:
1. What E and B fields (can be time dependent) will cause a charged particle to oscillate along a parabola
2. What can be done to include a drift/ group velocity so that the parabolas move in one direction.
 
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  • #2
Undulators give particle paths similar to (d): Alternating magnetic fields, the particles follow circle segments in each section. A fine-tuning of the magnetic fields can modify the path a bit more.
 
  • #3
Ok, so my research is basically modeling self replicating cracks with analog E and B fields. This means that I need an analytical expression (not experimental method).
 
  • #4
An analytical expression of what?
You can make up magnetic fields (or electric fields) that lead to parabolic paths of particles moving through that field.

Your question is quite vague.
 

1. What are E and B fields and how do they affect a charged particle's parabolic motion?

E and B fields refer to electric and magnetic fields, which are physical phenomena that exist in the space surrounding charged particles. These fields can exert forces on charged particles, causing them to accelerate and change direction. In the case of a charged particle moving in a parabolic path, the E and B fields can alter the shape and trajectory of the path.

2. How do the strength and direction of the E and B fields influence a charged particle's parabolic motion?

The strength and direction of the E and B fields play a crucial role in determining the behavior of a charged particle's parabolic motion. If the E field is stronger than the B field, the particle will experience a net force in the direction of the E field and will accelerate in that direction. If the B field is stronger than the E field, the particle will experience a net force in the direction of the B field and will follow a curved path. The direction of the fields also determines the orientation of the parabolic path.

3. How do the initial velocity and charge of a particle affect its parabolic motion in the presence of E and B fields?

The initial velocity and charge of a particle are important factors in determining its motion in the presence of E and B fields. A particle with a larger initial velocity will have a wider parabolic path, while a particle with a smaller initial velocity will have a narrower path. The charge of the particle also affects its motion, as a particle with a larger charge will experience a stronger force from the fields.

4. Can the E and B fields be used to control or manipulate a charged particle's parabolic motion?

Yes, the E and B fields can be used to control and manipulate a charged particle's parabolic motion. By adjusting the strength and direction of the fields, scientists can alter the shape and trajectory of the parabolic path. This is a useful technique in many fields, such as particle physics and medical imaging.

5. How are E and B fields related to each other in the context of a charged particle's parabolic motion?

E and B fields are closely related in the context of a charged particle's parabolic motion. They are both components of the electromagnetic force, which acts on charged particles. The strength and direction of the E and B fields are interdependent and can affect each other in complex ways. Understanding this relationship is essential for accurately predicting and controlling a charged particle's parabolic motion.

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