# Coulomb's Law: Electrostatic Force and Static Charges

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### The Idea

According to Newton's law of universal gravitation, any mass exerts a force on any other mass. Electric charges work in a very similar way. The farther away you get, the weaker the force. Because the electric force is so much stronger than the gravitational force, it is much easier to measure. This experiment explores the nature of the electrostatic force and establishes the basis for Coulomb's law.

### What You Need

• 2 pith balls or conductively coated Styrofoam balls (conductively coated ping-pong balls are also an option)
• 2 pieces of string about 16 inches in length
• movable ring stand with a pendulum clamp (or other horizontal support)
• small nonconductive post on a stand (the post should be a few inches in length and consist of a thin wooden dowel or a short glass or plastic rod)
• ruler
• rubber rod/wool pair (or equivalent) to apply a charge to the pith balls
• optional: light source to project the image of the pith balls onto a screen (an overhead project or LCD projector can serve this purpose)

### Method

1. Attach one side of each of the two strings to the pith ball.
2. Attach the other sides of the string to the pendulum clamp separated by a few inches, so the pith ball can swing in only one direction, as shown in Figure 96-1.
3. Attach the other pith ball to the nonconductive stand.
4. The swinging pith ball should be positioned so it can only swing closer to and further from the stationary ball.
5. Draw a reference mark on the bottom of the ring stand to indicate the rest position of the swinging pith ball without being subjected to any force other than gravity.
6. Vigorously rub the wool against the rubber rod to charge it up. Touch each of the pith balls to apply the same charge to them. Touching the two balls together will make the charges nearly equal, but it is not necessary to do this.
7. Start with a distance between the pith balls that allows the swinging ball to hang vertically.
8. Slowly bring the swinging pith ball closer until the repulsion between the two pith balls causes the swinging pith ball to move away from the stationary ball.
9. Measure how far the swinging pith ball moves horizontally. You may do this by observing from above and measuring the distance the ball has moved from the reference point.
10. Record the horizontal distance between the centers of each of the pith balls.
11. Repeat this measurement a few times by moving the swinging pith ball in a little closer.
12. The horizontal separation, x, between the unconstrained pith ball and its equilibrium position is a good indication of the force. (This can actually be worked out in terms of the force, but this is unnecessary to explore the key point of this experiment.) For small angles that the pith ball makes with the vertical, the electrostatic force is directly proportional to the separation from equilibrium.
13. The separation between the stationary ball and the equilibrium positions is designated as d, as shown in Figure 96-2. The total distance between the two pith balls is given by d + x. Make a graph of the separation from equilibrium, x, and the distance, d + x, between the balls.

### Expected Results

The closer the two balls get, the greater the force.

This relationship is not linear.
The closer the balls get, the faster the increase in force between the balls.
Specifically, this is an inverse square relationship.
Overall, this experiment works best on a day with low humidity.

### Why It Works

Coulomb's law states that the force (in newtons) between two charges, q1 and q2 (in Coulombs or C), separated by a distance, d (in meters), is given by:

where k is the Coulomb constant

= 9.0 × 109 m2/C2.

### Other Things to Try

Finding how many electrons are on a charged balloon.

Hang two balloons after first determining their mass. Charge them and touch them together, so they have roughly the same charge. The Coulomb force results in the balloons repelling and separating, as shown in Figure 96-3.

The number, n, of electrons on each of the balloons can then be determined from:

where q is the charge on 1 electron

= 1.6 × 10–19 C

k is Coulomb's constant = 9.0 × 109 m2/C2

m is the mass of each balloon and

is the angle the string of each balloon makes with a vertical line.

The Coulomb force can also be explored in the following simple demonstrations:

### Chasing a can

A charged rubber rod, such as the one previously used to charge the pith balls, induces a current in a can. This enables you to roll the can back and forth across the table, as if the rod were a magic wand.

### Bending water

A thin stream of water from a facet can be bent by a charged rod.

### Tape

The simplest of all is to take some transparent tape and adhere it to a table. After pulling it up, the tape will have acquired a charge that will be attracted or repelled by other nearby objects. Two similar pieces of tape acquire similar charges and are, therefore, repelled.

### Plasma globe/Sunder ball

This is a true "evil genius" prop that looks like something out of a Frankenstein movie. A small tesla coil produces a large voltage difference inside a glass bulb. This is similar to the way that charge builds up in clouds. Mini lightning bolts discharge through an inert gas in the bulb, producing an eerie glow. The electrons in the gas flow to the electrical ground harmlessly provided by a finger touching the outer edge of the glass as if the person touching the outside of the globe was a human lightning rod. This is safe to do because the current (amps) flowing is very small. See Figure 96-4.

### Further Analysis

Apply an Excel curve fit for the graph of the separation from equilibrium, x, versus the separation (d + x) between the balls. A scatter plot with the power option selected should indicate the best fit closest to –2, which is an inverse square relationship.

You could also plot x versus 1/(d + x)2. A linear fit to this graph would indicate an inverse square relationship between x (which is an indicator of the magnitude of the force) and d.

### The Point

The force between two charges is directly proportional to the product of the charges and inversely proportional to the distance separating the charges as given by Coulomb's law.