# Charged particles moving through electric fields

• Nissen, Søren Rune
In summary, the conversation is about deriving an equation for the movement of a positive ion through a quadropole, with the primary source being "Physics for Scientists and Engineers with Modern Physics" by Raymond A. Serway and John W. Jewett, Jr. The person is looking for pointers on where to start and mentions using the Biot-Savart Law. The conversation also touches on the use of the term quadropole, which could refer to either an electric or magnetic field. The person clarifies that they are referring to an electric quadropole and is trying to determine the particle's movement along the X and Y axes as a function of voltage, mass, and charge. They also mention that the charge distribution on the rods
Nissen, Søren Rune
I'm having some trouble trying to derive an equation for the movement of a positive ion through a quadropole.

The problem is that my primary source in this is "Physics for Scientists and Engineers with Modern Physics" by Raymond A. Serway and John W. Jewett, Jr. which has an excellent part on the subject of charged particles through electric fields*, but doesn't cover the subject of quadropoles, where the magnetic field is in flux.
(Or if it does, and you have the book, please point me at it, although that would make me feel very silly )

*pp. 725

I don't want you to derive it for me (at all. I want to learn this, yes?) but a short pointer on where to start would be nice

Last edited by a moderator:
Nissen said:
I'm having some trouble trying to derive an equation for the movement of a positive ion through a quadropole.

The problem is that my primary source in this is "Physics for Scientists and Engineers with Modern Physics" by Raymond A. Serway and John W. Jewett, Jr. which has an excellent part on the subject of charged particles through electric fields*, but doesn't cover the subject of quadropoles, where the magnetic field is in flux (Or if it does, and you have the book, please point me at it, although that would make me feel very sill )

*pp. 725

I don't want you to derive it for me (at all. I want to learn this, yes?) but a short pointer on where to start would be nice

Give this a try as a starting point. Then use what you know about the field from a single loop of current

If you don't know the single loop, try this

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c1

Thank you, I'll read it and go from there.

Hah, it seems like I have to go all the way back to the Biot-Savart Law to go anywhere near where it looks like something I recognize. Seems like a long night of reading is ahead :(

Possibly, we are speaking of different subjects, it seems. When I say "Quadropole" I refer to something that looks a little like the graphic below: Four charged rods, where the charged particle moves through them along the z-axis.

I'm trying to find out how the particles will move along the rod, which function I can apply with variables q, m, and AFAI remember, also U and v

Code:
 y
/|\
|      (-)
|   (+)   (+)
|      (-)
|
+-----> x

Nissen said:
Possibly, we are speaking of different subjects, it seems. When I say "Quadropole" I refer to something that looks a little like the graphic below: Four charged rods, where the charged particle moves through them along the z-axis.

I'm trying to find out how the particles will move along the rod, which function I can apply with variables q, m, and AFAI remember, also U and v

Your original post made reference to magnetic fields and "flux". Now you are talking about an electric quadrapole, which IS a totally different thing. You are right about that. Based on your diagram, You can calculate the fields along the path of the particle on the z axis. It sounds like the particle is constrained to move on that axis, so only the z component of the electric field is needed. Are the rods of finite length, or infinite, or are they really just charged particles? I suspect the latter, based on the use of the term quadrapole.

OlderDan said:
Your original post made reference to magnetic fields and "flux". Now you are talking about an electric quadrapole, which IS a totally different thing. You are right about that. Based on your diagram, You can calculate the fields along the path of the particle on the z axis. It sounds like the particle is constrained to move on that axis, so only the z component of the electric field is needed. Are the rods of finite length, or infinite, or are they really just charged particles? I suspect the latter, based on the use of the term quadrapole.

The reason my original post refers to "magnetic field" and "flux" is because I am, in fact, a damn fool. Sorry.

I meant "electric field" and "varies"

The rods are technically of finite length (It's a practical problem), but I've been informed that the results will be "close enough" if rods of infinite length are used. The particle has an (approximately) constant v in the z-axis direction.

I'm trying to find out how the particle moves along the X axis as a function of the voltage over the positively charged rods, as well as the mass and charge of the particle. I'm also trying to find the same for the Y axis, as a function of the voltage over the negatively charged rods, as well as the mass/charge of the particle.

I know it's either a sinus or co-sinus function, but I'm having trouble finding out where to start.

(Basically, I've been tasked with describing exactly what makes our mass-spectrometer work, and I'm having some trouble with the particle selector part, ie: quadropole.)

Can you assume a uniform charge distribution on each rod? That may not matter either as long as they have the same distribution and are symmetric relative to the motion. I assume, since you are talking about a mass spectrometer that you are looking at deflection forces that will take the particle off axis.

OlderDan said:
Can you assume a uniform charge distribution on each rod? That may not matter either as long as they have the same distribution and are symmetric relative to the motion. I assume, since you are talking about a mass spectrometer that you are looking at deflection forces that will take the particle off axis.

I believe the charge distribution will be uniform, yes, so the particles position along the Z axis can be ignored. They are symmetric along the Z axis. If no charge is applied to the quadropole, all values of m/q will move through the quadropole with no problems. However, by varying the voltage applied, only specific m/q values will be allowed through the quadropole, the rest will hit the quadropole and discharge.

Last edited by a moderator:
OK. If you assume infinitely long uniformly charged rods, the electric field for each rod is proportional to the charge density and inversely proportional to the distance from the rod. Adding up the electric fields from four rods of equal charge density becomes a vector addition problem. The way people usually do this is the treat the quadrapole as two dipoles, but that is probably only useful at some distance from the quadrapole. It might be easier for you to look at the potential, which will vary as the log of inverse distance from each rod. There is a section on the potential of an infinite rod here

http://www.pa.msu.edu/~duxbury/courses/phy294H/lectures/lecture10/lecture10.html

OlderDan said:

This looks very much like the exact thing I'm looking for. Thank you, OlderDan.

## 1. What are charged particles?

Charged particles are subatomic particles that carry an electrical charge, either positive or negative. Examples of charged particles include protons, electrons, and ions.

## 2. What is an electric field?

An electric field is a region in space where a charged particle experiences a force. It is created by other charged particles and can be either positive or negative.

## 3. How do charged particles move through electric fields?

Charged particles move through electric fields due to the interaction between the electric field and the charge of the particle. If the particle is positively charged, it will be attracted to the negative electric field and vice versa.

## 4. What factors affect the movement of charged particles through electric fields?

The movement of charged particles through electric fields is affected by the strength of the electric field, the charge of the particle, and the mass of the particle. A stronger electric field will result in a greater force on the particle, causing it to move faster.

## 5. How is the motion of charged particles through electric fields used in technology?

The motion of charged particles through electric fields is used in a variety of technologies, such as particle accelerators, cathode ray tubes, and electric motors. It is also crucial in the functioning of electronic devices and circuits.

• Introductory Physics Homework Help
Replies
14
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
26
Views
750
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
819
• Introductory Physics Homework Help
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
8
Views
388
• Introductory Physics Homework Help
Replies
1
Views
818
• Introductory Physics Homework Help
Replies
2
Views
776
• Introductory Physics Homework Help
Replies
5
Views
2K