Conservation of Charge to 2 Sig Figs

What is shows:

A neutral system of charges is rearranged...charge measured on one part is equal and opposite to the charge on another part. In that respect, this demonstration is not much different from the " 3 Sig Figs" demo in which voltage measurements are used. Conservation of charge is typically introduced in the first few lectures of an E&M course, before the concepts of voltage and capacitance are discussed. If voltage is the quantity measured, one needs to argue that this is also a measurement of charge, Q, since V=Q/C. Furthermore, if the voltages are the same, this means the charges are the same provided that the capacitances are the same. Using concepts unfamiliar to the students to explain how the demonstration works leave something to be desired. This demonstration is an improvement in that respect; electroscopes simply indicate the charge. It also utilizes more common household materials: a Fleece (which is usually 100% polyester) combined with either a cotton or silk shirt, or a woolen sweater, works very well.

charge conservation

How it works:

As the photograph shows, tall aluminum cooking pots replace the aluminum tubes in the " 3 Sig Figs" demo. They are insulated from the ground plane by Pyrex baking pans, giving them a capacitance of 60 pF with respect to ground.

The two items of clothing, e.g., Fleece and wool sweater, are placed in close contact in one of the pots. Next, each pot is fully discharged by a momentary electrical contact to the ground plane. One item of clothing is then removed and placed in the other (empty) pot. The electroscopes measure the charge developed as a result of this transfer; they should register the same magnitude of charge if charge is conserved.

The next step is to ascertain the polarity of the charges of the two pots and show that the two pots are oppositely charged. For this part of the demonstration one needs a charge of known sign for reference, which should have been introduced and used earlier in the lecture. PVC pipe rubbed with a cotton T-shirt works well; the PVC becomes negatively charged. Insert the charged PVC pipe into the pot containing the Fleece, without touching the pot or Fleece, and the connected electroscope will indicate an increase in charge. This means the pot containing the Fleece is negatively charged. In the same manner, insert the PVC pipe into the pot containing the wool sweater. That pot's electroscope will indicate a decrease in charge, meaning that it is positive.

An additional step may be taken to reinforce the concept of charge conservation. If one item of clothing is taken out of its pot and reunited with the other, both electroscopes will once more indicate zero net charge.

Two variations on the theme: (1) The triboelectric effect requires that the materials in contact be dissimilar. Consequently, if the two items of clothing are of the same material, no charge will be observed when they are separated; the electroscopes will indicate zero. If time permits, this is a worthwhile exercise. (2) The experiment may also be performed with just one piece of clothing, in which case the metal pot acts as the second material in the triboelectric effect. Metals are more-or-less in the middle of the triboelectric series and the effect is not as dramatic; only around 20 nC of charge (50 V for C≈400 pF) will be produced. To that end, more sensitive electroscopes will need to be used.


Although the demonstration is more finicky than the " 3 Sig Figs" version, it is well worth the extra effort. We'll instruct you on the techniques to practice beforehand.

Setting it up:

As the saying goes, "the devil is in the details," and the success of this demonstration is no exception. The following suggestions will help you secure success.

Clothing items and their handling: A fleece and wool sweater make for a reliable combination that works well, readily producing a couple of μC of charge and therefore a voltage of 2 kV for C≈1000 pF. However, other combinations have worked well too: (a) fleece and cotton T-shirt, (b) fleece and silk shirt, and (c) cotton and silk. Their polarities are as expected from their order in the following triboelectric series.

Rabbit's fur most positive (readily loses electrons)
Lucite (acrylic)
Human hair
Cat's fur
Sealing Wax
Hard rubber
Polyester (fleece)
Polystyrene (Styrofoam)
Saran wrap
Vinyl (PVC)
Teflon most negative (tends to attract electrons)

This list has been expanded from one published by C.D. Hendicks, Electrostatics and its Applications, edited by A.D. Moore (Wiley, 1973) Chapter 4, p 67. That author notes that the series is reproducible only in rare circumstances; cleanliness, humidity, and manufacturing differences affect the ordering.

In any case, fold the items of clothing to approximately the size of the bottom of the pot. Lay the sweater on the bottom and the fleece on top of the sweater. Press them together. Discharge both pots. Touch your own shirt sleeve and hand to the ground plane to remove stray charges before reaching back into the pot to retrieve the fleece. Do not touch the pot when you pull out the fleece. Immediately place the fleece into the other pot without touching that pot. Practice this well beforehand. If you hear crackling and discharges, you may very well be losing charge to somewhere not intended. In that case, lessen the amount of charge generated by reducing the intimate contact between the pieces of clothing, or use smaller pieces of the materials, or try any combination of the three suggestions below. If you are not getting enough charge separation, increase the contact area between the pieces of clothing. Note that what works brilliantly one day may not on another. You may very likely have to modify your technique depending on the humidity in the room.

Pots and supports: The voltage the pot will rise to depends on its capacitance, among other things. Too large a voltage will cause the air to break down in the strong electric field and produce undesirable discharges. One way to prevent that from happening is to increase the capacitance, as can be seen from V=Q/C. This is accomplished by decreasing the distance between the pot and the ground plane as well as choosing an insulating support with a higher dielectric constant. The following table lists capacitances for several combinations of materials and thicknesses.

Capacitance (pF) Material between pot and ground plane
42 25-cm tall glass beaker
60 8x8x2-inch Pyrex baking dish
140 1/2-in thick high-density polyethylene
220 1/2-in thick fiberglass
380 2-mm thick plastic tray
530 1/32-in thick Teflon sheet
600 1/16-in thick phenolic sheet
910 0.010-in thick Teflon sheet

As one might surmise from the table, a voltage reduction factor of 20 is probably about the best one can achieve with relatively common materials. That is to say, the capacitance of the pot sitting on a tall insulator can be increased by a factor of 20.

Another way of reducing the voltage is simply to reduce the magnitude of the charge separation generated in the separation of the items of clothing. One can (1) lessen the contact area by judiciously arranging the clothing, (2) use smaller items of clothing or swatches of cloth, or (3) choose a clothing material combination that results in less charge separation.

Checking the polarity of the charge: The general procedure was described above. Since there will be a large charge on the pot, it will take a considerable test charge to change the deflection on the electroscope. To that end, use a generous piece of PVC pipe; 1 to 2 inches in diameter and 2 to 3 feet long. Before the demonstration, clean the pipe well with alcohol to remove oils and other surface contaminants. In the demonstration, rub a good length of the pipe with the cotton shirt to maximize the amount of charge on it. It is prudent to have washed the cotton shirt beforehand; don't use fabric softeners in the water or "no-cling" additives in the dryer. When inserting the PVC pipe into the pot, lower it down the middle as far as you can without touching the clothing.