The mathematics may at first appear a little complicated, but it is actually a lot simpler than a real game I think. The complication arises from having to understand the gravitation and electrical forces involved for the simulation to make sense and from having to manipulate the equations to get a numerical result.

The experiment is tedious to perform in real life. It takes a long time to collect a little data; and the effort involved does not improve understanding. It involves a lot of squinting, focusing, and luck. I think it’s an experiment ideal for a simulation that would produce realistic data that you can then analyze.

Here’s a quote from an MIT lab manual. “The timing measurements are like a video game in which practice makes perfect. N repetitions of any given measurement will reduce the random error of the mean in proportion to N^1/2.”

 http://web.mit.edu/afs/athena/course/8/8.13/JLExperiments/JLExp_02.pdf

Background

The Millikan oil-drop experiment is a famous experiment done in 1909 that measured the magnitude of the charge on the electron. It works because the oil drop is so small that the change of one charge makes a noticeable difference. The experiment is a typical high-school or freshman physics lab. Millikan got the Nobel Prize in 1923 for this work.

You get an atomizer filled with oil, spray the oil as a mist into a two-level chamber. The drops fall through a little hole into the lower chamber.

Here’s a schematic picture from http://www68.pair.com/willisb/millikan/experiment.html 

Although the figure below does not show it, Millikan, pointed an x-ray source into the lower chamber to charge the drops. The lower chamber is between two capacitor plates. The drops are small enough that you have to use a microscope, and you often illuminate the lower chamber with a bright light (also not shown in the figure,)

This is more or less how Millikan did it. Today, people fill an atomizer with tiny latex balls, often have just one chamber, and skip the x-rays. Instead, you let the drop get its charge from rubbing against the nozzle of the atomizer or from encounters with stray charges left in the air by cosmic rays.

Here’s a photo from http://www.juliantrubin.com/bigten/millikanoildrop.html of Millikan's actual apparatus.

The experiment consists of varying the voltage (hundreds of volts) until you can get a drop to be rising at a constant rate. The distance between the plates varies from about 0.5 to 2 cm. More on the equations later.

There exist some simulations on the net. The URL http://www68.pair.com/willisb/millikan/experiment.html has the nicest one I’ve seen. It’s two-dimensional and a Java applet. That bottom line always reads 0V; I think it should increase as you increase the electric field. Here’s how  it looks.

Here’s a website that describes a version of the experiment using latex balls, one chamber, and no x rays.

 http://www.phy.davidson.edu/StuHome/MiLee/JLab/Ex4/title.htm

 You can buy an apparatus that makes the experiment easier and more reproducible. It even has a connection that allows you to project what the microscope seen onto a screen for an entire audience to see

 http://store.pasco.com/pascostore

The Experiment

Time the trips an oil drop makes over a known distance at various voltages. The falling velocities u_d (in the absence of voltage) are all the same because the oil doesn’t evaporate (early versions in Millikan’s lab used water droplets) and hence the weight is constant. The rising velocities (the drop rises when you turn up the voltage) vary with the charge q (which we know, but the experiment proves is an integral number of electronic charges, ne.)

The Equations

The symbols here all represent positive quantities so that the signs are explicit.

The force on a falling oil drop is

where w is the drop’s weight due to gravity, B is the buoyant force of the air and ku_d is the air resistance, which depends on the velocity. u_d is the downward velocity where the d means down. At terminal downward velocity the force is zero; the buoyant force and the air resistance exactly compensate for the weight. Note that the resistance is opposite to the weight because it is always opposite to the motion, and the drop is falling.

The force on a rising drop is

Note that in this case the weight and the air resistance have the same sign because the drop is rising and the air resistance is opposite to the motion. Also the velocity is a constant upward velocity so the subscript is u.

Replace w – B with ku_d and solve for q and you get

This looks deceptively simple. You set and measure the voltage V and measure the velocities. The electric field E is V/s where s is the distance between the plates. Fringe effects at the edges of the plates are negligible so the complication does not arise from that.

The complication comes from getting k, the Stokes constant. It depends on the radius of the drop and the air’s coefficient of viscosity η,

First of all we don’t know the radius of the drop. We do know it’s small, so small that the  equation above needs a correction because the radii of the drops is of the same order of magnitude of the mean free path of an air molecule which is 2.2 x 10^-6 cm.

High school versions often ignore these complications. You can read how to deal with them in an MIT lab manual at http://web.mit.edu/afs/athena/course/8/8.13/JLExperiments/JLExp_02.pdf

Last month I went to a PLUG meeting just by chance.

These meetings are on the first Thursday of every month and held in a conference room in the Student Union. Terrible place to park. You drive round and round, and it's often raining, and the parking meters are valid until 7PM nowadays, so you got to find one that will take enough time to let you walk those ten blocks, no ten-minute spaces allowed here.

You'd think I'd have lots of free time, not having worked in over five years, but I usually have something going on Thursday evenings. I had joined a reading group, and we read books about Microsoft's .Net Framework and meet on Thursdays. A few months ago we even took one of Microsoft's certification exams. Yes, we all passed; and yes, I thought the test was difficult in spite of all those teenagers that pass it and say they just studied for only a day or two.

But an email came in (I'm on the PLUG mailing list), and it said, well, David Mandel said (David is the president of PLUG) that this month's meeting was going to be on Tuesday, and it was special. Jeff Waugh and Mark Shuttleworth were winding up their North American tour, and PLUG even got a larger room because Jeff was going to talk about Ubuntu.

Of course, I had heard about Ubuntu. It was all over the mailing list, and I had just been to a book-signing party where the author's daughter had recently got married, and her husband had just started consulting, and I asked him what operating system he used, and he said Ubuntu. I had heard about Ubuntu, but placed it around the same level as slackware, one of those dog-brand Linux distributions.  When I had to run Linux, I fired up Red Hat 9 on one of my workstations that I set up to dual boot into either Windows XP or Red Hat. I thought of Red Hat or Suse or Turbo as the real distributions. Red Hat seemed to be teetering on the edge of being commercial, and so I was trying to come to terms with Fedora.

I had a lot to learn. The room was full of Linux geeks and gurus. They have that blended sense of arrogance and vulnerability, you know.  You can usually find a old guy with a paunch, unkempt gray hair, and sandals who stutters as well as students, geeks, and technical professionals.  Randal Schwartz was there, still looking young and clean-cut. I sort of recognized him; he was shorter than I remembered and had put on some weight (haven't we all). I heard him saying, “I've sold more books than any other O'Reilly author and I'm still working for a living.” “Debian is the operating system to use,” someone else said. Everyone within range nodded. Well.

Jeff's talk started with Gnome. To be honest I didn't know how he was affiliated with Gnome. The room treated him like a rock star, though, even video taping his presentation. I gathered that he had something to do with, may even have been in charge of, Gnome's release schedule. Didn't Linus Torvald (he lives around Portland but hardly ever ventures in public) recently say KDE was the Windows Manager to use? Anyway Jeff no longer has anything to do with Gnome (I think) and is now working at Ubuntu, and Ubuntu is a derivative of Debian.

Jeff's talk was long but very interesting. Lots of anecdotes. His excitement was contagious. PLUG only had the room until 9PM, and he talked until around 10PM, and there were people waiting in the hall outside.

We all got CDs on the way out. I picked up three packages. There was a package for X86, one for PowerPC, and one for MAC. Each package had two CDs. One is called the Live CD; the other is the install CD. The Live CD reminded me of Knoppix. You stick the CD in your computer and boot from it. You can run Linux directly from the CD and not modify your hard drive.  If Linux comes up, then you now that your hardware is compatible.

Jeff said in his talk that Ubuntu wanted the Install CD to be only one CD. When I downloaded Red Hat a while back, it filled up about five CDs, so I was skeptical. But the install CD is a really basic system. It doesn't even have gcc on it! The neat thing though is that once you install that basic system, you can use its update utility (called the Synaptic Packet Manager) to download and install what you need. Getting a gcc environment is executing just one command line.

PLUG routinely retires to the Lucky Labrador after the meeting for discussion and beer. It was late, after 10PM,  and I told Ron Braithwaite that I probably wouldn't make the Lucky Lab. On the way down the stairs, I asked a guy, heavyset and in a hurry. where Ubuntu got its money from, and he said he didn't know, but thought that much of the funding came from one person, Mark Shuttleworth. I thought, one person can't completely fund a company. Jeff had said that Ubuntu pledged to be always free, to be completely free, not a watered down free version and an expensive enterprise version. Follow the money, I thought, what's the agenda here? Suspicious person that I am.

So I did go to the Lucky Lab, a long walk to my car and a drive across the river to Hawthorn Bvld where Keith Lofstram explained to me that Mark was a very rich guy indeed, that he had gotten rich when he sold his company (the global certificate company Thawte), that he was one of the two guys in the world who actually paid to go up to the International Space Station. Keith said he paid $50M; I read later in an IEEE publication that he paid $20M. Yes, Mark could afford to fund Ubuntu. And will Ubuntu ever make money? “Oh, yes,” said Keith, “in support.” And he looked at me strangely as if I would ever doubt that.

Mark had stood in the back and off to the side when Jeff gave his talk. At the end of the talk, he came forward and Jeff introduced him as a professional dancer, and they did what Jeff called the Badger Badger Badger dance, which was very silly and lasted about thirty seconds. And now Mark was holding court at the Luck Lab's bar. He looks young and athletic, wearing jeans and a long leather coat.

I sat at a table with Ron Braithwaite and Jeff. Ron was explaining to me a customization I had to make to get Ubuntu to run under VPC (Microsoft's Virtual PC), something about Ubuntu assigning more bits for color than VPC did by default. Jeff said Ubuntu worked just fine under VMWare, the competitor for VPC. I asked about memory, and Jeff said give it at least 256M and that he ran with 768M; I said I was planning to give it a Gig, and he shrugged and said, “Well...” Unspoken was the question, Why are you bothering to ask? But what I had was 256M on a desktop that maxed at 1G and looking for an excuse to upgrade.

PLUG, although I often call it the Portland Linux Users Group,  actually stands for Portland Linux/Unix Group. Its website is http://www.pdxlinux.org/.