Comparing Electron Paths: The Impact of Magnetic Field Strength on Velocity

In summary, the conversation discusses the velocity of electrons on two different paths in a magnetic field. The speaker made a picture to better understand the concept and asks if the green path, which has a higher potential energy, would have a higher velocity. Another speaker suggests that the purple path, with a lower potential energy, may actually have a higher average kinetic energy and therefore be faster. The first speaker uses a diagram to show how often the electrons on the green path are moving faster than those on the purple path.
  • #1
Samson4
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I made a picture because I'd struggle to get out a question without it. In the picture all things are constant except the strength of the magnetic field. It is at two different values. We see 2 cycloid paths of electrons that starts at rest. The circumference of the large path is exactly twice that of the smaller path.

My question is, would the green path have the higher velocity away from the origin?
Although both paths are equal in length, shouldn't the green path be the fastest? I base this conclusion on the amount of work the electric field does in both cases.

Electron Path.png
 
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  • #2
I would say the purple path is faster because it's at a lower potential energy on average than the green. At first I agreed with your assessment, but then I noticed these were electron paths, so their potential energy increases in the direction of the electric field (since they're negatively charged). By that logic, the purple path should have a higher average kinetic energy and should be faster based purely on inspection. You could run a simulation or perform the time integral to double check.
 
  • #3
Twigg said:
I would say the purple path is faster because it's at a lower potential energy on average than the green. At first I agreed with your assessment, but then I noticed these were electron paths, so their potential energy increases in the direction of the electric field (since they're negatively charged). By that logic, the purple path should have a higher average kinetic energy and should be faster based purely on inspection. You could run a simulation or perform the time integral to double check.

I used the diagram to show how often the electrons on the green path are moving faster than the purple path. The yellow bars on the lorentz force line represent times when "green" electrons exceed the top speed of the purple electrons. I think this answers my question because now I realize that the red areas are when electrons in both paths are moving at the same velocity.
Electron Path2.png
 

FAQ: Comparing Electron Paths: The Impact of Magnetic Field Strength on Velocity

What is acceleration?

Acceleration is the rate of change in an object's velocity. In other words, it is the increase or decrease in speed or direction of an object over time.

How is acceleration calculated?

Acceleration is calculated by dividing the change in an object's velocity by the amount of time it took for that change to occur. The formula for acceleration is a = (vf - vi) / t, where a represents acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken.

What is the difference between positive and negative acceleration?

Positive acceleration occurs when an object's velocity increases over time, while negative acceleration (also known as deceleration) occurs when an object's velocity decreases over time. Positive acceleration is associated with speeding up, while negative acceleration is associated with slowing down.

How does acceleration relate to Newton's Second Law of Motion?

Newton's Second Law of Motion states that the force applied to an object is directly proportional to its mass and acceleration. In other words, the greater the force applied to an object, the greater its acceleration will be, and vice versa.

Can an object have constant acceleration?

Yes, an object can have constant acceleration if its velocity changes by the same amount over equal intervals of time. This means that the object's acceleration remains the same throughout its motion, either in a positive or negative direction.

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