Stuck with sticky tape
Advanced Physics for Teachers
Summer 2006
Adam Johnston & Gordon Haueter
A rather mundane means of separating charge can be done with standard “invisible” tape, commonly
used for gift wrap and other crafts. Obtain two pieces of tape, each about 10 cm long. Both pieces of
tape should have about half a centimeter of their ends folded over and stuck to themselves, so that you
have a non-sticky handle to grab the strips by. The first piece of tape should be stuck directly to a clean
table. Rub this piece so that you get rid of as many air bubbles between the table and the tape as
possible. With a pen or dark pencil, label this piece of tape, “lower.” The second piece of tape should be
stuck on top of the first piece, and the bubbles should be rubbed out. Label this piece of tape, “upper.”
You should make two such sticky tape pairs and stick them to the table.
Please make sure that each piece of tape has an end folded over for a handle; and, make sure that all
pieces of tape are cleaned off the lab tables before you leave the room!
Initially, these pieces of tape are neutrally charged. But, when the two pieces are slowly removed from
the table, and when one piece of tape is quickly peeled off the back of the other, charges should become
separated so that one piece of tape is the opposite charge as that of the other. Extra electrons get
stolen by one of the pieces of tape, leaving a net negative charge on this piece and a net positive charge
on the other piece. You can peel and re-stick the tape over and over again. The labels should remind
you which pieces of tape came from where.
Separate the tapes as just described, then bring them near each other and watch whether they
attract or repel. In addition to testing an “upper” and “lower” piece, compare this to two
pieces of “lower” and two pieces of “upper”. What do these forces tell you about the charge of
each piece of tape? What do they not tell you?
Inflate a balloon. When rubbed on your hair or on a piece of wool, fur, or similar material, this
balloon should have a negative charge. Given this information, determine the charge (positive or
negative) of each piece of tape (upper and lower). Describe your answer and how you
determined this answer.
Part II: Coulomb's law and the charge density of sticky tape
You are likely very familiar with Coulomb's law, which describes the force that any single charged
particle feels as a result of the presence of another charged particle:
FE = k
q1q2
r2
(1)
Here q1 and q2 are the (net) amounts of charge on the two particles, while r is the separation distance
between them. In ordinary SI units, r is measured in meters and the charges are measured in units of
coulombs (C). The constant, k, has a huge value in these units: k = 9×109 N·m2/C2. This means that two
one-coulomb charges separated by a distance of one meter would exert forces on each other with a
strength of nine billion newtons (roughly the weight of a cubic football field of water). Needless to say,
the net charges on your sticky tapes are only tiny fractions of a coulomb.
A single proton or electron has a charge whose magnitude is equal to 1.6×10 -19 coulombs. Note, by the
way, that Coulomb's law for the force between electrostatic charges is mathematically similar to the
Newton's law for the gravitational force between two massive objects.
Your next task is to determine the amount of charge on an “upper” or “lower” piece of invisible tape.
To do this, you will use Coulomb's law and an analysis of all the forces involved that “balance”
electrostatic forces and allow a piece of tape to sit in equilibrium. You will also need to make a few
approximations.
Hang one piece of charged tape (freshly peeled) from a horizontal wooden meter stick. Hold another
similarly charged piece of tape at both ends and bring it close to the piece of hanging tape. You should
witness the hanging tape feeling a force and orienting itself several degrees away from the vertical. Note
that the force of gravity keeps this piece of tape from lying horizontally. You will need to consider this
force of gravity in the analysis of this problem.
With your understanding of the situation and a careful analysis of the forces involved (you will need to
draw and analyze a force diagram), you can calculate the number of extra or missing electrons on one
piece of tape. To help you in your quest you have tools such as a protractor, balance, and ruler (or
meter stick). You may also harass your instructor. Most importantly, you have your lab group to discuss
your methods and ideas with.
Yup. Go ahead. Do this. Talk it over. Draw a picture. Label some forces. Make some
measurements. You can even make an approximation or two. Solve for the number of charges.
Some other things to consider and do once you’ve counted these charges:
Although the number of elementary charges that you've solved for may seem extremely large, it
is very small compared to the total number of molecules on the surface of a piece of tape.
Calculate the ratio of charged molecules to total molecules. Assume that the molecules form a
two-dimensional grid system in which each molecule is 3×10-10 m away from any other
molecule. (If your calculations show that there exist more charged molecules than total
molecules, you should realize that something has gone awry.)
If the density of charge on a surface is greater than 5×10-9 C/cm2, then the charges will be able
to produce a “spark” into the air molecules surrounding the tape. Calculate the density of
charge on the surface of your tape, and compare it to this “sparking density.” Does your
calculation seem reasonable? Explain.