Experiment 6
Coulomb's Law

General Introduction

You've probably heard more than you wanted to know about Coulomb's Law and why it's important, either in class or from your recitation TAs; also, by now you should have read my thoughts on what the purpose of these labs is. In any case, it might be a good idea to take a look at the sections on what's important and what things to watch out for; both from a theoretical point of view and from a "how do we get this done right/quickly/at-all" point of view, they should hopefully help.

What's Important in This Lab

• The form of Coulomb's Law turns out to be supported by a simple experiment (but keep in mind it took Coulomb a few years to do...).
• Humidity in the air causes slight conduction, and so reduces static electricity over time. You knew this from experience in life, but in this experiment you can actually calculate the amount of drop-off.
• Plotting functions of curves (namely, logarithms) can be a useful tool for looking for certain behavior (namely, power laws or exponential behavior).

Hints and Tips for making this lab a better experience

• The room is quite warm and very dry, so you if you wear contacts but have glasses, you'll probably want to wear your glasses so your contacts don't dry out during the lab...
• 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...
• We pointed out in lab lecture that vibrations ruin the precision of your results. This includes vibrations made by the handy electric timers you have to do the timing. So, even though it's a bit of a pain, it'd be better to have one partner hold the timer so it's not on the table.
  Another choice that's good is to put the timer on a spare stool, so you don't have to hold it but it doesn't vibrate the table.

Part I (of the lab)

• Most of the setup should have been done for you; however, you should go ahead and clean the spheres, and make sure the light is aligned and focused correctly. The lab manual's instructions are pretty clear on how everything should be set up.

Part II

• The damping setup (glass container with water and polyethylene glycol) will have been set to provide the "critical damping" mentioned in the lab manual; you can check that if you want, but for the purposes of the experiment I don't mind if you just accept that it's at the critical point.
• One important thing to watch for is that the metal "vane" attached to the torsion balance is completely below the surface of the water mixture. Of course, then the wire that holds the vane still sticks up through the surface, but it's smaller and will have less surface-tension effects to mess up the response.
  If you need more water to make the level high enough, let the TA know.
• The other important thing in setting up the damping is that the vane should be able to travel over a wide range without hitting either side of the glass container. If it does hit, it'll stick or at least provide an external force on the sphere that would pretty well overwhelm the electric force that we're trying to measure here!

Part III

• This is the part where you measure how fast charge leaks off the spheres. You'll repeat this part exactly at the end of the experiment.
• The lab manual says to "keep increasing the charge" until you get an initial deflection of about 25cm; however, once you put some charge on there then it's harder to get the spheres to touch again to re-equalize charge. My advice is, if you didn't get enough displacement, then ground the spheres and try again, rubbing the rod a little more this time; same thing if you got too much displacement.
  Careful about getting too much charge on them, though; that can mess up your alignment of the balance and damping setup. When you're rubbing the rod, once you start hearing the static-electricity crackles, you're at about enough charge to put onto the spheres.
• The lab manual says to record the time at every cm. This gives not very many data points; better is to record it at every half centimeter, or better yet, do that and at some nice even multiple of seconds (like every 15 seconds or so).
• How long should you let it go? Well, this curve is one you're going to use to correct your other data points later in the lab. Essentially, you will be recording for all your other measurements the time at which the deflection was such-and-such. So, what you're really measuring is the deflection given that some of the charge has leaked off the spheres. What you want to deal with and plot is the deflection as if all the original charge were on there and none had leaked off, so you'll need to read the correction off of this plot.
  What this all means is that you have to record this for as long or longer than it will take you to do any of the other measurements in Parts IV and V. Use your judgment on that -- half an hour is a bit long, but 10 minutes would give you a good idea of how the charge leaks off...

Part IV

• You get more accurate results if you bring in the grounded test sphere to touch the movable sphere (the one on the slide indicator) such that the line between them is perpendicular to the line between the movable and torsion spheres, in other words, touch the test sphere to the side of the movable sphere, as seen from the torsion balance.
• Make sure you ground the test sphere before touching to again halve the charge, or various bad things will happen (you never know what charges the test sphere will have picked up by being set down on the table).

Part V

• Nothing new here, really; same deal. Make sure to use the timer or you'll have trouble correcting your data later on...
• Oh, sorry, there is one thing. You might, if you have time, do this twice, and the second time test 20,15,10,5 cm in that order, and see if it makes a difference. (They did this this way in an older version of this experiment.)

Part VI

Data Analysis

• You can do the graphs after you leave the lab; you'll probably spend enough time as it is taking the data.
• In #3 in the Data Analysis section it says to plot ln[ deflection (decay-corrected) ] versus separation. This is wrong, and will not give you the curve you're looking for. You need to also take the ln[ separation ] , and use that as the y-coordinates instead of just the separation.
• The lab manual is really confusing about how to do the averaging of the two decay-correction parts, and about how to do the correction itself (actually, it doesn't say how to do the correction). The TAs will talk about that at the beginning and at the end of the lab, so make sure to listen up and ask questions if you're still confused.
  The only reason I'm not putting up here, now, how to do it, is that I need some time to talk to the other TAs so we can agree on a uniform way to explain this and have you do it. There are a couple of subtle options, and we want to all be saying the same things!

Things to Watch Out For (safety-type issues)

• Not much to seriously worry about; this is a pretty safe lab.
• If the leads aren't already hooked up to the transformer when you come in, make sure the transformer's unplugged before hooking up the leads. It's only 12V, but can still give you a bit of a shock.
• Be a little careful around the torsion wire, as it's brittle and if it snaps can fly around.