Figure 1

In this lab you’ll observe a typical large-scale manifestation of the forces between electrically charged objects. We’ll pit the force of gravity against the electrostatic force to determine the amount of charge on each of a pair of small identical spheres – pith balls .

The operation of the Virtual Electrostatics Lab is very simple. A certain amount of charge is acquired by a charging rod when this rod is rubbed against the charging cat which has volunteered to take part in this experiment. Part of this excess charge is passed on to two initially neutral conducting pith balls which then share it equally.

The pith balls are immediately forced apart by the Coulomb repulsion between them. They swing back and forth, gradually slowed by air resistance, until they are in static equilibrium as shown in Figure 1. If there was just one ball present its excess charge should be a spherically symmetrical surface charge. Because they are similarly charged – both negative – conductors placed near one another their excess charge would actually be skewed outward away from one another. To minimize the effect of this the balls have been made very small. The balls will be considered small enough relative to their separation

distance that the redistribution of charge on them is insignificant. We’ll assume that the charge on each ball takes on a spherical distribution. So why does that matter?

𝐹 = 𝑘 𝑞1𝑞2



Coulomb’s Law

In Coulomb’s Law, is the distance between the charges, q1, and q2. But our pith balls have charges spread all over their

surfaces. So the force is actually the sum of all the forces between all the individual charges – electrons and protons – and each pair has a different r. Fortunately, if the (excess) charge is distributed evenly on a spherical surface, the force is the same as if the charge was all located at the center of each sphere. So is just the distance between the centers of the pith balls.

We now want to find to find the charge on one of the pith balls. Since they’re equally charged – they have an equal number of excess electrons – we’ll just call the charge on either ball, q.

Your goal is to find q, (in Coulombs.)

So how’s that going to happen? Let’s try out the apparatus first to get a clearer idea of what’s going to happen.

Figure 2 shows how the apparatus looks at start up. Refer to Figure 1 for terminology. The parallel plates that are omitted from the figure are not used in this lab.


  1. Notice that the charge number and charge on each ball in the info box both read zero.

The charge number is a reference number that you’ll record for grading purposes. It’s meaningless otherwise. The charge on each ball is initially zero since they are initially uncharged.

  1. Click anywhere on the charging rod. Keeping an eye on the info box, drag the rod so that the ball on its end moves across the cat. The more you drag it across the cat the more the charge # increases. The ball is fully charged when the number reaches 120. Try it.

  2. Drag the charging rod until the charging ball touches the tip of the grounding rod. Poof. Back to zero. You can also move the grounding rod to touch the charging ball to discharge it.

  3. Recharge the rod to a charge # > 50. Now drag it until it its ball touches either of the pith balls. Some charge has now been transferred. The pith balls equally share it.

  4. You’re going to need to know the deflection angle, θ , between either ball and the vertical. That’s what the protractor is for. Move your pointer over the protractor until the pointer changes to a hand (or whatever). Click and drag it up near where the strings are tied and release. It should snap in place.

Figure 2

Hold down the space bar until the curved edge of the protractor almost reaches the pith balls. You should now be able to read the angle between either string and the vertical line at 0°. This deflection angle is the angle you’ll be using in your calculations. You can shrink the protractor back down with the <CTRL> key and drag it out of the way when you don’t need it.

Note: You can right-click or <CTRL>-click (Mac) to zoom in at any time. But while zoomed in you can’t drag anything.

  1. To measure the separation between the centers of the balls, click on the ruler, somewhere to the left of 35 cm, and drag it to a convenient place beneath the pith balls. You’ll want to measure the distance between their centers when taking data.

  2. You may also want to measure the length of the pendulum – the distance from the tie-off point to the center of a pith ball. Clicking to the right of 35 cm and dragging up or down will rotate the ruler. You can then align it with the string.


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