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Charged particles moving through electric fields 
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#1
Apr2505, 09:31 AM

P: 40

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 


#2
Apr2505, 09:57 AM

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http://hyperphysics.phyastr.gsu.edu...agquad.html#c2 If you don't know the single loop, try this http://hyperphysics.phyastr.gsu.edu...curloo.html#c1 


#3
Apr2505, 09:57 AM

P: 40

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



#4
Apr2505, 10:01 AM

P: 40

Charged particles moving through electric fields
Hah, it seems like I have to go all the way back to the BiotSavart Law to go anywhere near where it looks like something I recognize. Seems like a long night of reading is ahead :(



#5
Apr2505, 11:06 AM

P: 40

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 zaxis.
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



#6
Apr2505, 11:57 AM

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#7
Apr2605, 02:15 AM

P: 40

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 zaxis 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 cosinus function, but I'm having trouble finding out where to start. (Basically, I've been tasked with describing exactly what makes our massspectrometer work, and I'm having some trouble with the particle selector part, ie: quadropole.) 


#8
Apr2605, 02:46 AM

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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.



#9
Apr2605, 03:22 AM

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#10
Apr2605, 09:31 AM

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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/cours...lecture10.html 


#11
Apr2605, 11:06 AM

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