Electrostatics

1. Law of Charges

Prior to doing this section you should have done a lab called Zap! Read From the Lab... for a summary of observations you should have made in that lab.

One key observation from that lab was the Law of Charges. This is illustrated in the following movies and animations. In each, the clear strip of plastic gives the pith balls a positive charge. The white plastic strip gives the pith balls a negative charge. We'll learn how later. (Pith balls very light spheres made of soft wood.)

Here we see a positively charged plastic strip giving a positive charge to each of two pith balls. As a result they repel.

Here we see a negatively charged plastic strip giving a negative charge to each of two pith balls. They also repel. From these first two movies we see that objects with like charge repel.

This time we have given the pith balls opposite charges. In this case they attract. This illustrates the second part of the law of charges, that objects with opposite charge attract..

You might also note that we see evidence that charge is being transferred from one ball to the other after contact. Just what is this evidence?

We summarize this behavior in a rule often referred to as the Law of Charges. It's a bit of an archaic term, but let's use it since it's handy to have a name for this behavior.

 The Law of Charges Likes repel and unlikes attract.

Here's one more look at this behavior.

1. Two charged bodies are some distance apart and experience a repulsive force. If the charge on one body is positive, the charge on the other must be
 positive negative
2. From our experience in the lab we also know that attraction can occur if one body is charged and the other uncharged. We'll return to that puzzle later. Just keep it in mind.

2. The Bohr Atom

So what is the source of all these electrical effects? Actually we don't exactly know. Whatever their source is, it exists at too small a scale for us to see. But over the years we have developed some useful models that help us codify what we observe. None of these models is assumed to be the final one; each just builds on the previous. The model that will serve all our needs for the phenomenon we're going to study was created in the early part of the 20th century. It's called the Bohr model of the atom and it's the one that everyone learns in grade school.

Based on his experiments and those of others, Niels Bohr described matter as being made of atoms each of which consist of a tiny nucleus with a positive charge, surrounded by orbiting electrons which carry a negative charge. We call the carriers of this positive charge protons. We now know that the nuclei of all atoms larger than Hydrogen also contain neutral particles which we call neutrons.

The particles in the nucleus-the protons and the neutrons-have approximately equal masses, about 1.67x10-27 kg. The electron's mass is about 9.11x10-31 kg.

1. The mass of a proton or neutron is (very) roughly _____ times that of the electron?
 0.001 100,000 2000 .0002

It is difficult to assess the actual size of any of these particles, but a typical nucleus has a radius on the order of 10-15 m. The relatively large orbits occupied by the electrons have radii on the order of 10-10 m.

Here's an animation that shows the basic idea. It shows a Helium atom with its two neutrons, two protons, and two electrons.

On your screen, the nucleus is about 1 centimeter across. If the proper scale was used, about how large should the diameter of the electron orbits be?
 10 cm 100,000 cm 10-5  cm 500 cm

The proton and electron carry exactly the same amount of electrical charge. We call this quantity the elementary charge, e. The proton has a charge of +e; the electron's charge is -e. The + and - signs refer to the two types of charge we learned about in the lab.

The Helium atom shown is in a neutral state, the state in which we normally find it on the earth. We say that an atom or molecule is neutral if it has equal numbers of protons and electrons. If one or more electrons is added or removed then it is a negative or positive ion respectively.

We will consider adding and removing protons and neutrons to form different elements and isotopes in our study of nuclear physics. Such events have nothing to do with the simple electrostatic phenomena we are currently considering. We will consider the nucleus to be off limits. Any movement of charge will be done by electrons or ions, the protons and neutrons will stay put in the nucleus. This means that currents flowing through wires or any other solids are made up entirely of electrons. In liquids and gases, positive or negative ions can carry charge.

Whatever is carrying the charge, we always find that the amount of charge will be some integer multiple of e. We say that charge is quantized. We only find exceptions to this rule when we break apart protons and neutrons into their components called quarks. A quark carries a charge of ±1/3 e or ±2/3 e.

3. Charging and Charge Conservation

So what was going on microscopically in the lab when we were rubbing things together and making them exert forces on other objects? How does this relate to our model of the atom? And are we making charge when we charge objects up?

Experiments like those you did in the lab and their possible interpretation gave scientists fits for centuries. We know today, that when we rubbed the paper and plastic together, charge, carried by electrons, was moving from one material to the other. The material that lost the electrons was left with an excess of positive charge (assuming that it started out neutral), and the other material gained electrons and as a result acquired a negative charge.

 Charging by Friction Rubbing two dissimilar objects together will always result in their having opposite charges. The electrons will transfer to the object with the greatest affinity for them.

So we didn't really create charges, we just moved them. This is the transfer of charges, not the creation of charges.

Let's make sure we're clear on the two ways in which we use the word charge. When we say that charges are moving along a wire, we are just referring to the moving electrons in a general sort of way. When we talk about the charge on a body, we are referring to its net charge. The net charge is the amount of excess of negative or positive charge.

Ex. A negative helium atom might have one extra electron. It has 5 charges, 2 protons and 3 electrons. It has a (net) charge of -1e.

So we can transfer charges around to make things charged, but can we actually create charges? Well, in most cases, we can't. But in certain nuclear processes we can, but not one at a time. Whenever we create a negative charge, a positive one is created along with it for a net charge change of zero. One example is called electron pair production. If an X-ray of the right energy passes near a massive nucleus, the X-ray can just disappear and an electron and its antiparticle, a positron will just poof into existence! The reverse can also occur.

Now all this is beyond the scope of our work, but what you need to know is that we can move charges around and in extreme cases we can create and destroy them, but the net charge in a system never changes.

 The Law of Conservation of Charge: Net charge can be neither created nor destroyed.

When we rub the plastic and paper together we're just moving charges around, not creating them. The same charges continue to exist; they have just been separated. If we return the charges to where they started, all the electrostatic effects disappear since a positive charge produces electrical effects opposite that of a negative charge. From a distance it appears as if charges had been destroyed!
This was the insight that took many minds to figure out. Can you see why Ben Franklin suggested the (+) and (-) terminology?

1. If some object is given a negative charge, then it follows that some other object acquires an equal amount of positive charge. 2. The Law of Conservation of Charge implies that charges can't be created or destroyed. 3. We've found that the electrostatic force is similar in many ways to the gravitational force. But consider these two facts. In the Bohr atom, the electrical force is responsible for holding the electrons in orbit. The gravitational force is responsible for holding the moon in its orbit about the earth. How do you explain this? What happens to the effect of the other force in each case?

4. The Electroscope-Detecting Charge

In the Zap! lab we found ways to detect the presence of charge and determine its sign using simple materials. The electroscope is a more sophisticated tool that will allow us to extend our observations.

This image shows one type of electroscope. Notice the labeled parts. You'll need to become familiar with these terms. The term "leaves" comes from an earlier model that had two thin strips of gold foil that came to be known as leaves. Instead of leaves of gold, our model has a thick metal support and a light strip of aluminum that rotates on an axle. Only the aluminum strip moves, but we will still refer to the metal support and the aluminum strip as the "leaves." We will refer to their motion as "spreading" and "converging" as the gold strips did in the original electroscope.
(Incidentally, the trouble is not in your set. This figure doesn't move. How archaic!)

Here we see the electroscope's behavior when it's given a positive charge by a plastic strip.

And here's the electroscope with a different plate. This time it's being given a negative charge.

So what's going on here? To help you see the microscopic details of what happened, here's an animation showing an electroscope being given a negative charge.

You've seen the behavior of the electroscope when it's given a negative charge. If there are any details you missed, you should go back and play it again until you get a clear idea of what happens and why. Once you've done that you're ready for questions like these:

1) What will happen now if the negative strip is moved away from the electroscope after charging it?
 The charges and the leaves will stay put. The leaves will converge completely, that is, the aluminum strip will stand upright. The charges will jump back onto the strip. Some of the excess electrons will move up to the plate and the leaves will fall a bit.

2) What will be the charge on the scope after the the strip is removed?
 Negative Positive Neutral
3) What will be the charge on the plate?
 Negative Positive Neutral
4) What will be the charge on the leaves?
 Negative Positive Neutral
5) Rerun the electroscope charging animation, but this time assume a positively charged plastic strip. Answer each question in the animation and explain what would happen in each step of the animation.
Hint: The macroscopic results are the same, but microscopically, there are some important differences. Don't forget, the positive charges can't move!

Close but no Contact

Here are a couple of movies showing a somewhat different behavior. See if you can explain what's happening microscopically based on what you see. Remember, the white strip is negative and the clear strip is positive.

Negative strip near scope

Positive strip near scope

6. Is charge being transferred between the plastic strips and the electroscope? 7. Charge isn't transferred (except in the case of sparks) unless there is contact between the strip and the plate. But obviously the leaves are becoming charged since they are spreading. What's causing the leaves to become charged?
 Electrons are moving down to the leaves in the first movie and up toward the plate in the second movie. Protons are moving down to the leaves in the first movie and up toward the plate in the second movie. Electrons are moving up toward the plate in the first movie and down toward the leaves in the second movie. Protons are moving up toward the plate in the first movie and down toward the leaves in the second movie.

You may have found the above questions very challenging. This is because the world at this scale is foreign to you, but with a little work learning the basic behaviors of charges you can predict what will happen just as easily as you deal with the world on our scale.

Determining the Charge of an Object with the Electroscope

Let's take this new apparatus out for a spin. In the following animation a rubber rod which has been rubbed with fur is brought near a negatively charged electroscope. We'd like to use the scope to test the sign of the charge on the rubber rod.

8) Was charge transferred between the rod and the electroscope? Unless a spark occurs, we'll only find charge transfer when direct contact is made.

9) In the previous animation it was stated that the leaves spread due to the movement of electrons downward into the leaves. Positive charges moving upward from the leaves would produce the same result. Would this be an equally acceptable explanation? Remember, only electrons move in solids! The protons are bound in the nucleus by the strong nuclear force.

5. Polarization and Grounding

Let's re-visit a movie we saw earlier to introduce a new concept.

1) The electroscope was initially neutral. Was the electroscope as a whole ever charged during the movie? Since the scope was initially neutral and no charge moved to or from it, it remained neutral. Its leaves, however became negatively charged. Electrons, repelled by the negative strip, moved from the plate to the leaves. The plate became equally positively charged due to its loss of electrons. We say that the electroscope became polarized. Incidentally, polarization can also occur for charged bodies.

 When charge is distributed so that one part of an body is positive and another part is negative, we say that the body is electrically polarized.

2. What was the sign of each part of the scope when the positive strip was near the plate

 Negative plate, positive leaves Positive plate, negative leaves

We'll return to polarization later. It has many important applications.

When we use our electroscope we always need to know exactly what state it's in before we start. We've learned how to give it a negative or a positive charge. How about a neutral condition? We know it's neutral if its leaves are hanging vertically. (Actually, we can't tell neutrality from a slightly charged state with this apparatus, but we won't worry over this.) How could we get the scope in this neutral state? Watch the following movie to see how a positively charged scope is neutralized.

What the finger (actually my entire body) did was called grounding the electroscope.

 Grounding Electrical Ground - earth or some other large conductor that can receive or supply charges (usually electrons) without significantly affecting its own electrical condition. Grounding - making electrical contact between a charged body and ground. Charges flow between the body and ground in a direction that "equalizes crowding" thus nearly neutralizing the small body.

We know that the scope was made neutral just by touching it with a finger, since the leaves hung vertically afterwards. But what was the mechanism? What happened electrically? How about grounding a negatively charged scope. It looks just the same macroscopically, but the electrons move in the other direction. For a look at the details, watch the following animation which shows what happens when a wire is connected between a charged electroscope and ground.

If you didn't catch the difference between the two animations you just observed, go back and run them again. Notice the direction of motion of the electrons in each case.

Your body works well as a ground for small charges. In your house, ground wires connect directly to the earth. In the U.S. we call such wires "ground" wires. The British call them "earth" wires.

One question that we've not considered is how to determine the sign of the charge on an electroscope. Before going further you need to tackle this question and test some of your ideas about electroscopes in the lab using the Rezap! lab.

Read From the Lab... for a summary of observations you should have made in that lab.

6. Charging Methods

Earlier we learned that we could give opposite charges to dissimilar materials by rubbing them together. We called this charging by friction. You should have plenty of experience with this. When you slide out of a car seat you may get a shock when you touch the metal car body. Your clothes and the car seat get opposite charges since they have different affinities for electrons. Whichever material had the greater affinity for electrons became negatively charged. The other material became positively charged.

This doesn't work so well with conductors since they tend to conduct away their charge before much builds up. Instead, we mainly notice this effect with insulators.

Charge produced by friction with insulators is always localized since the charges can't move about on an insulator. Look at this movie and see the effect. Only the end of the plastic strip is rubbed with the sheet of paper. Notice how the bits of paper collect there.

This tendency of charges to stay put on insulators leads to the static cling on clothes just out of the clothes dryer. When these clothes, which are mainly insulators, become charged by being rubbed together, the charges tend to stay put. Various products have been created to address this problem. Some products add a thin conducting layer to the clothes. This allows charge to conduct away to the metal dryer.

This passing of charge from the highly charged clothing to the neutral dryer is called charging by conduction or contact.

The most interesting method of charging is by induction. You learned about it in the ReZap lab.

 Charging by Induction Bringing a charged object near a conductor & then grounding the conductor will cause electrons to move on or off the conductor. (The electrons move from or to ground, respectively.) As a result, the two objects will become oppositely charged.

This one is easier said than understood. Let's look at some examples. In this movie, a negatively charged rod is used to give a positive charge to an electroscope. Be sure to note not only what happens, but in what order. Also notice how the charged strip is used to test for the sign of the charge on the electroscope.

Did you catch all that? Then try this one.

1. To charge the electroscope by induction, which should be removed first?

 the charged rod the connection to ground

Let's make sure you're clear on how charging by induction works with an animation.

Please note that the excess charges on the conducting ball in the previous animation were spread over the outside of the ball, even if the ball is solid. We'll learn why later.

7. Polarization Revisited

We learned earlier that a neutral body can have some of its charge redistributed into positive and negative regions if a charged object was brought nearby. We say that the uncharged body becomes polarized by induction. By this we mean that the charged body doesn't actually supply the charges, rather, its effect is to redistribute the charges already in the neutral body. (Actually the body doesn't have to be neutral, but we'll assume that it is for simplicity.)

Understanding this, we can now explain our ability to attract a neutral can to our plastic strip in the Zap lab.

Attraction due to Induced Polarization - Conductors

The law of charges says that likes repel and unlikes attract. In the Zap lab you found that sometimes a charged body attracts a neutral body. Is this a third part of the law? Watch this movie to remind yourself of how this worked.

To understand how attraction between a charged and a neutral body works you need to realize that matter is composed of particles that have charge. It is these particles that are attracted to each other, not their parent bodies as a whole. The force on the parent body is just the sum of these individual forces. Watch this animation and see if you can deduce an explanation. You'll need to go beyond the law of charges to include another factor besides charge.

So, how do we explain this attraction of a neutral conductor? The answer lies in the distance between the charges. It should be clear from your experience that electrostatic forces drop off with distance. If a body is polarized by a charged body, the side with like charge is farther away from the inducing body than the side with the opposite charge. Whenever this occurs, the two bodies will always be attracted.

How does this explain the attraction of the metal can in the lab?

Here's an interesting extension to the previous phenomenon. Watch this movie and discuss the extra events at the end. How do you explain how we go from attraction to repulsion? Draw a sequence of diagrams to explain each step.

Attraction due to Induced Polarization - Insulators

It's time for you to do a little demonstration. Inflate a rubber balloon. Rub it against a soft fabric like a cotton shirt. This will charge it up. You will find that the balloon will be attracted to everything around you even though most of those things are neutral. Try it. We know why it's attracted to conductors, but how about insulators. Bring the balloon near another uncharged balloon or some other piece of plastic. There will be a strong attraction. While you're figuring this one out, park your balloon on the wall of the room. It will probably stay quite contentedly even though the paint is a pretty good insulator.

So, how do you explain this one?
Here are some clues. There is again some re-distribution of charge even though there is no conduction of charge. How can charges be re-distributed even if they never leave their home molecule? Think of yourself as one of the many electrons zipping around a nucleus. If a large negative charge came nearby, how might that affect your motion? How might your orbit be affected?

The nearby charge distorts some of the electron orbits so that the atom itself is polarized in that the average location of its negative charge which is at sort of the center of mass of the electron orbits is a bit offset from it's nucleus, it's positive charge carrier.