### 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
Message:
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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
direction.

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
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
charged.)

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

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

Again, I'm just making sure you have your thinking cap on! If you aren't
please feel free to e-mail me at mwnet@swbell.net. There's a lot more to
this than you might think!

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.)

-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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