Measuring the charge on a piece of tape
To measure the size, in Coulombs, of the electric charge
transferred from a tabletop to a piece of tape.
What's the Point?
Electricity can be very important in the interaction
between two objects, at their surface of contact.
It is especially important at small scales,
for objects smaller than a centimeter or so.
In this experiment, you'll see electric forces bend
two pieces of tape.
Cutnell and Johnson, Chapter 18.
Note especially the discussion of the electric force between
two charged particles:
- scotch tape
- digital analytical balance
- Measure the mass per unit length of tape
- Cut a strip of scotch tape about 10 cm long. Measure its length
and width carefully.
Use the balance to measure the mass of the tape in grams.
Calculate the mass per unit length of the tape,
in grams per centimeter.
You'll need this to determine the mass of some pieces
of tape later on
- Create two strips of tape
- Cut two strips of roughly the same length, around 10 cm long.
Place each strip sticky-side down on a table near the edge,
so that about one quarter of the strip hangs over the edge.
Try to arrange the pieces so that the same length of each
one is stuck to the table.
Measure that length carefully.
Use a marker to draw a line on each piece of tape
where it touches the edge.
- Place charge on each strip
- Using one hand for each strip, grab the ends which are hanging
over the edge of the table. Try to grip the tape as close
to the mark as possible.
Pull the strips up and off the table.
As you break the bond between tape and surface, the tape
will pull some charged particles off the surface.
Each strip will end up with an electric charge, and the sign
of the charge (positive or negative) will be the same for
Hold your hands well apart, so that the strips don't come
close to each other. Make sure that the strips
are face-on to each other.
- Move the strips close enough to exert significant electric forces
on each other -- but not close enough to touch
- Have your partner hold a ruler horizontally, and hold your hands
that that you can measure the distance between the two strips.
Slowly move your hands together. Watch the strips. They should
hang straight down at first, but as they approach each other,
the electric charges on their surfaces will repel each other.
Measure the separation D at which the strips bend
away from each other at approximately 45 degrees from the
vertical. You may discover that one strip bends more than
the other; if so, then find the distance at which the
angles away from the vertical add up to 90 degrees
(e.g. 30 degrees away from the vertical for one piece
and 60 degrees for the other).
Be sure to measure
D as the distance between the top sections of the
tape, held by your fingers.
- Make a simplification
- Calculating forces on extended objects such as these strips
of tape is difficult. It is much simpler to deal with
ideal objects: "point masses", tiny little particles which
contain all the mass and charge of a real object, condensed into a
In this case, we can replace the real situation, shown
above, with an reasonable substitute: two charged point masses,
each at the center of the hanging strip, connected to
the top section of tape by a massless little string.
The mass of the ideal ball, m, is the same as
the mass of the hanging section of the tape.
The charge of the ideal ball, q, is the same as
the charge of the hanging section of the tape.
The length of the string, L, is just half
the length of the hanging section.
- Draw a free-body diagram of the ideal situation
- Pick one of the little balls in the idealized situation.
Draw a free-body diagram which shows the direction of all
the forces acting on it. (Hint: there are three forces).
Use your diagram to set up two equations describing
the net force on the little ball: one in the vertical
direction, one in the horizontal direction.
- Figure out the size of the charge on each strip of tape
- You should be able to solve these equations for
the charge on each little ball, q (you may
assume that it is the same size on each ball).
This charge is a decent approximation to the actual charge
accumulated on each strip of tape when you ripped it off
Express this charge in both Coulombs and in electrons.
Okay, so you know approximately how much charge was transferred
to a piece of tape. But can you also answer these questions?
- Does the tape pick up negative charge (electrons) or positive
charge (protons)? Is it possible to tell, in theory?
Is there any practical way to find out?
- Suppose that the tape grabbed little chunks of stuff from the tabletop,
each containing e, one electron's worth of charge
(either positive or negative).
What fraction of the atoms along the surface of contact
contributed some charge to the tape?
Did every atom on the tabletop contribute one chunk of charge,
or only a few of all the atoms touched by the tape?
You'll need to compare the number of units of charge e
to the number of atoms on the surface of the tabletop
touched by the tape.
To a very rough approximation, atoms in the table are spaced
in a grid, with about 0.2 nm between each atom.
- We assumed that the amount of charge on each piece of tape
is the same (you may assume that it is the same size on each ball).
Is this a good assumption or a bad assumption? Support your answer.
Last modified 11/18/2003 by MWR