MadSci Network: Physics

Re: Any fields around an electron beam?

Date: Sat Jan 22 00:29:47 2000
Posted By: Matthew B. Weyerich, Technical Coordinator,ES&R Dept., CPI Corp.
Area of science: Physics
ID: 947643171.Ph

Hi, Jesse!

A beam of electrons travelling through space can be thought of as a 
"current". Wherever you find electric current, you will find a magnetic 
field. (The electrons are responsible for the field, not the conductor.) 
So, yes, there should be a magnetic field around a beam of electrons.

What can we say about the field around a beam of electrons?

Well, it will follow the Right-hand rule, which the McGraw-Hill Dictionary 
of Scientific and Technical Terms defines as:

"For a current-carrying wire, the rule that if the fingers of the right 
hand are placed around the wire so that the thumb points in the direction 
of current flow, the fingers will be pointing in the direction of the 
magnetic field produced by the wire".

Careful here! You may have noticed this definition is for a 
"current-carrying wire", and that it mentions the magnetic field "produced 
by the wire". A beam in space wouldn't involve a wire. Also, I just told 
you the conductor is not responsible for the field. What gives?

Just making sure you have your thinking cap on, actually. The mention of 
the wire is important in understanding the direction of current flow. Other 
statements of the rule note it applies to a POSITIVE charge, only. You are 
talking about electrons, which are negatively charged. The rule still 
applies, but requires a little thought if we are to come up with the right 

Try this: Grab a pen. Pretend it is a wire with a current flowing from the 
top of the pen to the point. If you grasp the pen…as you'd grasp the rung 
of a ladder… with your right hand so that your thumb points along the 
barrel to the point, your fingers will be wrapped around the pen in the 
direction of the magnetic field created by the current. (If I hold the 
point of the pen with my left hand, so the pen is horizontal, my right-hand 
fingers go above the pen and wrap around. My right thumb points toward the 
pen point, and toward my left hand.)

Now, pretend the pen is a beam of electrons travelling from top to pen 
point. How would you grasp the pen? (Remember, electrons are negatively 

The electrons in a beam would travel from the top of the pen to the point. 
If the Right-hand rule applied to negative currents, you'd grab it the same 
way I described above. However, the rule is for POSITIVE charges. If you 
look at a schematic you'll see "positive charges" are always on the 
opposite side of the circuit from "negative charges". You can think of them 
"flowing" in a direction opposite that of "negative charges". So…

You'd grasp the pen so your thumb pointed in a direction opposite the flow 
of electrons. (If you hold the point of the horizontal pen with your left 
hand you'd turn your right palm toward the ceiling and place it "under" the 
pen barrel. Your right thumb would then point away from the pen point, and 
away from your left hand.)

Confusing? You can thank Benjamin Franklin for that. You see, Ben did lots 
of the early work on electricity. He didn't know about electrons, so he 
assumed electric "force" traveled from "+" to "-". He had a 50/50 shot at 
the right answer, but his guess was 100% wrong. (Perhaps he worked on this 
AFTER his famous kite & key experiment?) Nonetheless, much of electronics, 
including schematics, and the Right-hand rule, still follow Ben's 
descriptive convention.

(By the way: I put in the "produced by the wire" bit just to demonstrate 
you can't believe everything you read! The conductor may have some effect 
on the magnetic field, but it is not necessary for the generation of a 
magnetic field. The definition, as presented, is ambiguous…that's why I 
cited it. Nit-picky, I know, but you have to be careful these days!)

What else can we say about our "beam"? Depends upon how detailed you want 
to get, and how you want to look at it.

For example, what constitutes a "beam"? A trillion electrons a second? A 
hundred? Ten? How about just one? (All qualify as "currents".) How would 
you quantify each?

The math gets really complex, especially because electric and magnetic 
forces are described in different terms. (Different squiggly-signs and 
Greek letters in calculus.) I won't even try to detail it all here. 
However, it can be described, and, has been. (E-mail me if you need 
details. Otherwise, search for Ampere and Faraday's contributions to 
Maxwell's equations.)

As for your questions about protons and neutrons: what are protons, and, 
what are neutrons?

You can think of protons as "ions", or, "molecules" with an excess of "+", 
or, "-" charge. Figure out the charge and direction of travel and you'll be 
on your way to understanding what kind of magnetic field they will display. 

Neutrons are entirely different, though, as they are "neutral". (They 
aren't thought of as "charged" in a "+", or, "-" sense.) These guys WILL 
NOT generate a magnetic field, per se.

(Bonus…what about positrons? I thought of these because I thought you might 
not have meant to ask about protons, but, rather, "anti-electrons". If you 
think carefully about what I've told you about "currents" you can easily 
come up with your own answer to this.)

Again, I'm just making sure you have your thinking cap on! If you aren't 
clear about what I've tried to explain, or, if you just need more info, 
please feel free to e-mail me at There's a lot more to 
this than you might think!

I hope this has helped answer your questions. If not, please tell me, and 
I'll put MY thinking cap back on for you!(Maybe I've got mine on 
"backwards", considering all the reciprocal relationships involved here. If 
I've messed something up, please make sure to let me know.)

Your MadSci,
-Matt Weyerich

P.S. - Most sincere thanks to Tom Rudnick, CPI Corp., for his help with 
this. Tom is an AMAZING Electrical Engineer, so, he knows a lot about 
electrons and how they behave. He was kind enough to photocopy and EXPLAIN 
a few pages from Elements of Engineering Electromagnetics, [Prentice-Hall] 
by N. Narayana Rao (See pp. 64-65, Chapter 2, "Maxwell's Equations in 
Integral Form", sec. 2.4, "Ampere's Circuital Law".) Tom took Dr. Rao's 
class,and was, therefore, able to explain the graph to me as a "potato"…as 
Dr. Rao apparently does. This worked incredibly well for me, as I best 
think of things when they are put in the most simple, and silly terms.(I 
understand and appreciate calculus in applied physics, and engineering. I 
just don't like all the "squigglies"!) Best thing was, Tom listened 
patiently while I wrapped my "silly-brain" around this, and helped me 
understand even more than I'd asked about. That's the way to learn, as far 
as I'm concerned!  Thanks again, Tom! :)

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