# Measuring the charge on a piece of tape

#### Purpose

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:

#### Equipment

• scotch tape
• ruler
• digital analytical balance

#### Procedure

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 each strip. 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 small ball. 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 the tabletop. Express this charge in both Coulombs and in electrons.