Particle in constant electic and magnetic field

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Discussion Overview

The discussion revolves around the motion of a charged particle, specifically a proton, in the presence of both constant electric and magnetic fields. Participants explore the implications of these forces on the particle's trajectory, including the effects of gravity and the complexity of the motion involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes the initial motion of a proton being influenced by an electric field, suggesting it would move toward a negative plate due to electric force.
  • Another participant recalls that in a cathode ray tube, an electron can pass through undeflected when both electric and magnetic fields are present, prompting curiosity about the underlying reasons.
  • A participant challenges the previous claim, indicating that the scenario described is not the general case and suggests a more detailed approach using the Lorentz force equation.
  • One participant proposes a step-by-step method to approximate the particle's motion by calculating changes in velocity over small time intervals.
  • Another participant mentions that the motion of the particle would not be constant and questions whether this would result in a spiral trajectory.
  • A later reply confirms that the net force would change due to the non-constant velocity of the particle, suggesting a potential spiral path, but also notes that there could be loops depending on the relative strengths of the electric and magnetic fields.
  • Participants share diagrams to illustrate their interpretations of the particle's motion, seeking feedback on which representation is more accurate.

Areas of Agreement / Disagreement

Participants express differing views on the specifics of the particle's motion in combined electric and magnetic fields. While some agree on the complexity of the motion, including potential spirals or loops, there is no consensus on the exact nature of the trajectory or the conditions that dictate it.

Contextual Notes

The discussion highlights the need for advanced mathematical tools, such as vector calculus and differential equations, to fully describe the motion of the particle under the influence of both fields. There are also references to specific applications, like the magnetron, which may not be fully explored in the context of the original question.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of physics, particularly those curious about electromagnetism and the dynamics of charged particles in fields.

Decan
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This isn't really a homework question, just something to satisfy my curiosity but if it belongs in the homework section, I really apologize and if the mods could move it to that section, it would be much appreciated.

Anywho, in class we talked about a particle accelerated by an electric field generated by capacitors. It then leaves through a hole and enters a constant magnetic field. That got me thinking, what if there is a constant magnetic field AND an electric field acting on the object at the same time?

http://img442.imageshack.us/img442/406/physicsix5.png

Above is my interpretation of what would happen. Let's say a proton is released, it would travel toward the negative plate because it is accelerated in that direction because of the electric force. The motion of the proton in a magnetic field would generate a magnetic force and cause the proton to move in a circle. The net force on the object = magnetic force + electric force. My question is, how would the partice move? I know the manetic force and the electric force are components of the net force but can anyone help me understand the direction of movement? Since the particle does not have constant acceleration (so no constant velocity), is it possible to figure out the velocity of the particle? Here's what I think...

F net = qvB + qE = ma; so v = (ma-qE)/qB but since the acceleration is changing constantly, would this be instantaneous velocity? If so, is the trajectory created by this velocity also changing constantly (since Fmag = mv^2/R)?

Finally, what if gravity was involved? Now the net force has 3 components...but I can't imagine/figure out how the partice would move. The professor is out of town and will be for the next few days. I think that understanding this would really help me on the exam so any help would be greatly appreciated. Thanks!
 
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From memory, I looked at a few study guide diagrams, if both an electric field and magnetic field were present in a cathode ray tube an electron would pass through undeflected.
 
I wonder why that is...
 
f3, that'd be Thomson's experiment rather than the general case.

Decan, the simplest (brute force) approach to this problem (using your F net = qvB + qE = m[itex]\frac{\triangle v}{\triangle t}[/itex]) is to consider one [itex]{\triangle t}[/itex] at a time, draw the particle's velocity initially, calculate the initial change in velocity, use that to deduce the approximate position and velocity a moment later, then re-calculate the force and change in velocity at this later moment, and step by step you'll draw out the shape of the motion. (Within a few steps you'll understand why physicists use computers so frequently.)
 
I don't believe fnr15's memory is serving correctly here. You are on the right track but you need more sophisticated tools (namely vector calculus and differential equations) to describe the motion mathematically. For instance, the Lorentz force is written as
[tex]\vec{F}=q\vec{E}+q\vec{v}\times\vec{B}[/tex]

The situation you describe is actually used in the magnetron, the famous pulsed microwave source that powered radar during WW2 and that now powers your microwave oven. Take a look at Fig. 4 in
http://www.radartutorial.eu/08.transmitters/tx08.en.html"
which shows the motion of electrons between the negative inner conductor (cathode) and positive shell (anode), where the potential difference is usually on the order of 10kV. A magnetic field (oriented perpendicular to the paper) makes the electrons spiral.

Here's a picture of a magnetron like that used in GE microwave ovens
http://www.gallawa.com/microtech/magnetron.html"

In addition to the simple fields you envisioned, a magnetron adds local RF fields in the cavities. You can read down the page to see how it works.
 
Last edited by a moderator:
So, would the net force then constantly change because the particle does not have constant velocity? If so, would the motion of the particle be in a spiral?
 
1. Yes
2. Almost. There will be a net motion along the field between your capacitor plates, so the path can have loops.
 
I haven't worked this out exactly, but I think you can get either depending on the relative strengths of E and B.
 

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