Coulomb’s Law
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The Force Between Two Charged Spheres
Pre-lab Exercise: Read this handout. Review the Graphical Analysis of Data.
Introduction
As we have just seen in class similarly prepared charged objects repel. In this lab we investigate how the
magnitude of the repulsive force depends on the distance between the objects. We might expect that the force
gets weaker as the distance increases, and gets stronger as the distance decreases. Coulomb's Law describes
the mathematical relationship between force and distance for two point charges. In this experiment we will
determine how the force between two similarly prepared, charged pith balls depends on the distance between
their centers. We will assume that the force varies as F = Cr n , in which r is the distance between the centers
of the pith balls, and determine n.
The photo below shows two silver pith balls inside a wooden box. The right hand pith ball is suspended
by a light string, barely visible in the photo. The left hand pith ball is mounted on the end of a long insulating
rod attached to a wooden block seen to the left of the box. When the balls are similarly prepared, as shown,
the pith ball on the left exerts a force F on the hanging pith ball, pushing it to the right by an amount x. By
moving the wooden block we can vary r, the distance between the balls, and see how x is affected.
Also visible in the photo are a ruler and a mirror. The ruler is used to accurately measure the position of
each pith ball, and the mirror is used to eliminate parallax errors, as will be explained in lab.
String
Pith balls
Fig. 1 The pith ball on the left exerts a force, F, on the hanging pith ball,
causing it to be displaced from the vertical.
Procedure
1. Make a schematic diagram of the apparatus.
2. Measure and record the equilibrium position of the center of the uncharged, hanging pith ball. Be sure
you know how to use the mirror to avoid parallax error.
3. Charge the acrylic rod by rubbing it with the vinyl sheet. To charge the hanging pith ball, touch it with
the charged rod. The pith ball will probably be attracted at first, but once charge transfers from the rod to
the pith ball it will be repelled. Charge the rod again by rubbing with the vinyl sheet and touch it to the
Coulomb’s Law
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mounted pith ball.
4. There is a vertical line on the wood block holding the mounted pith ball. Position the block so that the
mark is at 6 cm on the ruler mounted outside the box. Check that the position of the ball, as measured on
the ruler inside the box is also at 6 cm. If it isn't, consult your instructor. Measure the position of the
hanging ball. If the hanging ball has moved at least 0.5 cm from its equilibrium position, record the
positions of the two pith balls. Otherwise, you will have to try adding more charge to the pith balls.
5. Move the mounted ball and note the behavior of the hanging ball.
6. Using a free body diagram and an analysis of the forces determine how you can find the power n in the
above expression for the force. [Hint: Relate F to x and use graphical techniques.] You can use the small
angle approximation for the deflection of the hanging mass from equilibrium. Consult with your
instructor as necessary. Describe your method in your lab notebook and clearly label measured quantities
on your schematic diagram.
7. In taking data please note the following: Work as quickly as possible so that any loss of charge during the
experiment is minimized. (You may need to re-charge the system prior to starting.) About 2.0 cm
increments work well. Take data in both directions, until the mounted ball is back at 6 cm. [Explain why
this is a good idea.]
8. Enter your position data into Excel. Following your method, use Excel to determine the power of r, i.e. n.
Please include uncertainty.
9. Quote your result in standard form. Discuss your result in terms of what you expected and in terms of
random and systematic errors.