Experiment 8
Electron Beams
General Introduction
This lab experiment is, like the last one, a
verification of a fundamental constant in physics. Last time what we verified
was Coulomb's Law; this time, we are verifying that the ratio of the electron's
charge to its mass is a constant (see below).
This experiment is quick and quite easy -- a nice contrast to the Coulomb's
Law experiment that was long and confusing. I'll encourage you to stay just
a little bit and do the second part of it, too, because it's fun as well and
just as easy, and you get to twiddle more knobs and make cool shapes on a
screen -- but, as Prof. Douglass said in the lab lecture, the second part is
in fact optional for P114 folks.
Theoretical Ramblings (feel free to skip this)
(See this on a separate page)
What's Important in This Lab
There is basically only the one concept that you need to come away from this
lab with a good appreciation of, and that's the fact that the ratio of the
charge to the mass is, for elementary particles like electrons, a fundamental
constant, and that it's something (at least in the case of the electron) that
we can pretty much directly measure with a straightforward experiment.
Also, if you do the second part (which I recommend), you'll get a little bit
of experience with finding your way around an oscilloscope, and see some of
their usefulness!
Hints and Tips for making this lab a better
experience
- Make sure to record the uncertainty associated with each type of
measurement, along with some note about what gave rise to that
uncertainty. You'll need it for doing the data analysis, and you
need it to be complete...
- Some of the numbers that Prof. Douglass put up on the board for the
values of some fundamental constants were incorrect! So here
they are, for real.
Note: Some of these might be familiar, but are probably given
here to more digits than you might see listed in your textbook. It's
okay in your lab writeups to use the approximations that are listed
in your textbook, if they're a few digits shorter, but these are the
currently-accepted best-known values for these things:
- elementary charge: 1.60217733 x 10^-19 C
- electron mass: 9.1093897 x 10^-31 kg
- e/m ratio: 1.75881962 x 10^11 C/kg
- mu_0 (permeability of free space): 4 x (pi) x 10^-7 H/m
(this is cited in the lab manual, but with a horrible lack of
precision, since this number is defined to be this and
so it's known exactly!)
With the exception of the last one, the above numbers are known to
between 0.3 and 0.59 parts per million; so you don't have to worry
about uncertainties related to these constants in your writeup!
- There was some confusion at the lab lecture about whether you are to
measure the coil radius yourself or assume it's given. Professor
Douglass seems to think that as a class you have problems doing simple
multiplication; I know that nobody gets into med school without
knowing how to multiply, so I'm going to ask (those in my sections) to
measure the coil radius and calculate the B/I factor for your own
setup. As a part of the data analysis, though, you should compare it
to the value given in the lab manual and see if it matches to within
the expected error...
- There are many parts of the lab manual for this experiment that are a
little confusing, so please read on below.
Part I (of the lab)
- The lab manual is just plain wrong about which way to orient your setup
to avoid having to deal with the Earth's magnetic field. Since you
don't want extraneous unknown magnetic fields parallel to
the Helmholtz-coil field that you're setting up, you should align the
apparatus so that the line connecting the centers of the two coils
points east-west. Don't worry, I'll point out which
direction it is, and I'll most likely already have the setups turned
for you.
By the way, see the theory page if you're
interested in knowing a little more about the Earth's field and why
it's actually not pointing out one side of the room!
- Definitely wait the five minutes for the equipment to warm up; you'll get
much better numbers!
- The units will go up to 500 volts, and/or 3.00 amperes, and will nicely
refuse to go any higher rather than shorting out. Keep this in mind
when you pick voltages/currents to use for taking data. The lab manual
says to test 200V and 300V and one other voltage. I tried 250V, and
found it worked fine; if you like, pick some other reasonable voltage.
- You should get a value for "e/m" for each current setting at each voltage
you do; in other words, if you do 9 current settings for 3 voltage
settings as it says in the lab manual, you'll have 27 values for e/m.
I'd like you to find the average of these for each voltage setting,
and compare the estimated error with the standard deviation; however,
just go straight to the e/m value, don't bother calculating (rxB) as
it says in the lab manual.
- For figuring out estimated error, the lab manual says to ignore the error
in voltage and current calibration. Sure, go ahead and assume for now
that there's no systematic error in those; but since the
displays only show you a certain number of digits, there's got to be
some estimated error in knowing these quantities...
Part II
- The scopes we're using are, of course, Tektronix scopes, not
"Tektro Mics" as someone mis-typed in the lab manual...
- If you pull out slightly the sides where the handle goes into the scope
body, you'll see you can rotate it and then lock the handle at various
angles. You can use this to put the handle down so the oscilloscope
faces upwards to make it easier to see.
- The lab manual says nothing about proper or safe oscilloscope procedures.
This I consider really annoying, as these are pretty sensitive
instruments and it's relatively easy to damage them, so here's a little
basic checklist:
- Make sure the power is turned off; plug in the scope.
- Turn the "intensity" knob all the way down.
- Set the switch directly under each channel's scale knob (the one
with choices "AC"/"GND"/"DC") to GND.
- Turn the scope on.
- Push in the button labeled "P-P AUTO" (it's over to the right, in
the "triggering" section).
- Make sure the time-scale knob is set to something reasonable (in
the ms range, for instance).
- Set the "vertical mode" knob to "CH1".
- Slowly turn up the "intensity" knob until you can see a line on the
screen. Keep it dim, but bright enough that you can see it.
- Adjust the "focus" knob, if necessary, to get the line as sharp as
it will go.
- Adjust the "CH1 (up/down) POSITION" knob to put the line on the
center horizontal line.
- Make sure all red "CAL" knobs are turned all the way clockwise.
- There's lots more fun stuff to do with oscilloscopes. If you have any
questions, ask me during the lab and we can play a bit...
Part III
No, no, I'm kidding; you're done.
Really. It's over. There's only those two parts.
Things to Watch Out For (safety-type issues)
- If you take the "box" cover off while the tube is on in the first part,
be warned that there is high voltage (up to 500V) in the leads that
go up to the cathode inside the tube.
- If you run the oscilloscopes too bright for very long, you're going to
burn out their tubes.
Copyright 1997 Michael J. Banks
(mbanks@pas.rochester.edu)