5.1.1: Illustrations

Illustration 1: Charge and Coulomb's Law

What is charge? Charge is a property of certain subatomic particles and is not a substance that can be transferred from one particle to another. Particles either have charge or they don't. When we say that we are charging an object, what we really mean to say is that we are transferring particles that have charge from one macroscopic object to another macroscopic object.

Experiments done over \(200\) years ago by Benjamin Franklin and others led to the arbitrary assignment of the name "negative" to the property of those particles that are transferred to hard rubber when it is rubbed with wool. Franklin did not, of course, know about elementary particles. We now know that the particles being transferred in rubbing are electrons. We also know that electrons are not the only particles that have the property of charge. You have probably heard about protons, but there are many other particles with nonzero charge. When charging an object, we could say that we are "massing" a ball with electrons rather than "charging" a ball. Such literalism would be correct, but awkward. What we are interested in, after all, is the charge property that is being imparted to the ball by the electrons. Restart.

Use the animation to create three like charges at \(x = -1\text{ m}\), \(x = 0\text{ m}\), and \(x = 1\text{ m}\). You can do this by entering the position in the text box and clicking the add button (position is given in meters). What is the net force on the middle charge? It is zero because the forces from the other two charges cancel. Now move one of the outer charges around. Is the force on the middle charge still zero? No. The force between two particles always lies on the line between the two particles, is attractive or repulsive depending on the signs of the charges, and varies as \(1\) over the square of the separation distance (\(1/r^{2}\)).

Add a few charged particles with the same magnitude of charge (and with both positive and negative sign), and move them around by click-dragging them. Use the text box for charge to add the charges. The arrows on the screen show how the particles interact with each other by showing both the magnitude (relative size of the arrow) and direction of the electrostatic force.

Now reset the animation and create two charges with different amounts of charge. Notice the differences and similarities in the force vectors shown on the particles. Also look at the case in which the charges have the same polarity (same sign) and opposite polarity (one positive and one negative). With only two charges, the forces acting on the two objects are always equal and opposite.

The animation allows you to create particles of either polarity and to create particles with any amount of charge. Nature, on the other hand, is constrained. As far as we know, particles can only be created so that the total charge does not change. That is, if a positive particle is created, then another negative particle must also be created. Furthermore, the magnitude of the charge that is created must be an integer multiple of a fundamental unit. Although these restrictions are most apparent in the microscopic world, they manifest themselves in the macroscopic world. For example, a battery requires that equal numbers of charged particles enter and leave the two terminals. (Otherwise the battery would be creating one type of charge.) In the final analysis, all that we can really say is that certain particles have a property called charge that enables them to repel some particles and attract others. If two charged particles repel, then a third charged particle will either repel both particles or attract both particles.

Illustration 2: Charge and Mass

This Illustration shows a fixed charge at the center and one or more test charges (depending on whether you choose Animation 1 or Animation 2) that move under the influence of the fixed charge. Run the animations and observe the motion of the test charges. You can reset the animations and click-drag the test charges. Can you determine the sign of the fixed charge? In other words, is the fixed charge positive or negative? Can you determine the mass of the test charge? What can you say about the force between the fixed charge and the test charge? How is the interaction similar to and how is it different from Newton's universal law of gravitation? These questions are of fundamental importance to physicists who must try to determine the charge, mass, and other physical properties of elementary particles using trajectories produced in experiments at high-energy particle accelerator laboratories throughout the world. Restart.

A test charge is defined as a positively charged object whose charge is so small that it does not influence other objects, including other test charges. Therefore, in these animations we assume that the fixed object has much more charge than the test charge(s) so that the motion of the test charges is determined by the Coulomb interaction with the fixed charge. This is similar to having a number of satellites in orbit around Earth. We usually ignore the gravitational attraction between satellites and only consider a satellite's attraction to Earth, and maybe the moon and Sun, when we calculate the satellite's trajectory. In Animation 2 what are the directions of the forces on the red and green test charges? The directions are radially outward just as it is for only one test charge in Animation 1. Remember, we are ignoring the effect of the test charges on each other's motions.

In Animation 2, if the test charges have the same mass, can you determine which test charge, red or green, has the bigger charge? If the mass is the same, comparing the accelerations will tell you about the force and, therefore, the charge on the test charge. What if the test objects had different masses as well as different charges? Would this change your answer? The ratio of charge to mass is now proportional to the acceleration, and this ratio affects the motion that you observe. In general, it is not easy to untangle the combination of charge and mass on the motion of charged particles. Early experiments using particle trajectories were performed in \(1887\) by Joseph J. Thompson and led to the realization that electrons are charged particles, but it took another \(24\) years before Robert A. Millikan was able to separate the effect of charge from that of mass.

Illustration 3: Monopole, Dipole, and Quadrupole

The Coulomb force law predicts that the force of attraction (or repulsion) falls off as \(1/r^{2}\) as the distance between two charges increases. But nature rarely provides us with point charges. Molecules, for example, consist of positive and negative charges bound together by nonclassical forces that can only be explained using quantum mechanics. But electrical forces are still present even if positive and negative charges are bound, and we can develop useful force laws that approximate common charge distributions. Restart.

This Illustration allows you to study the force between a movable test charge and orientations of one, two, and four fixed charges. The force between the test charge and a single point charge, known as a monopole, obeys the Coulomb force law. A system consisting of two closely spaced charges of opposite polarity is known as a dipole. Two dipoles placed next to each other form what is called a quadrupole. What can you say about the differences in the force vs. distance graph for the three cases? Does one or more of the plots show a force that decreases at some rate other than \(1/r^{2}\)? If so, why isn't this a violation of Coulomb's law? Why does the force drop off more quickly with the addition of more charges?

When you add up the forces due to several charges, the net force experienced by other charges may be different from \(1/r^{2}\) depending on the orientation, magnitude, and sign of the charges. For the dipole, the separation between the positive charge and the test charge is almost the same as the separation between the negative charge and the test charge. If the separations were the same, the two charges would be on top of each other, and the net force on the test charge would be zero. But these separations are not quite identical. When we add up these forces, for the dipole we get a net force that goes like \(1/r^{3}\) and for the quadrupole we get a net force that goes as \(1/r^{4}\).

When you get a good-looking graph, right-click on the graph to get a copy of that graph in order to contrast it with the other animations.

Illustration 4: Charging Objects and Static Cling

These animations model materials with charges (red = positive and blue = negative). The arrows show the forces between particles. Restart.

There are a number of ways to charge objects. You may be familiar with what happens when you rub a balloon against your sweater. Due to the rubbing, the balloon becomes negatively charged. It will stick to the wall or the ceiling, but the wall and ceiling are neutral. Why will it stick to neutral objects? Run the balloon animation to see. The model shows the negatively charged balloon near a neutral ceiling. While neutral, there are charges in the ceiling. The ceiling is not chargeless; it just has an equal number of positive and negative charges. What happens to the neutral ceiling? This effect is called polarization (when the charges in an atom get slightly distorted due to other nearby charges).

Another way to charge an object is by induction (to induce it). First, look at the case where the left plate is positively charged and the right plate is neutral (equal number of positive and negative charges) as in this animation. Why do the charges separate as they do in the right plate? Charges move according to the forces they experience (like charges attract and opposite charges repel). Suppose we give the charges on the right a place to go (specifically ground) as shown in this animation? What happens? Why?; Neutral pairs of positive and negative charges separate from each other due to the nearby positive charge. Then the positive charges on the right leak off the grounded plate.

When an object is charged (like a computer screen), other objects can stick to it. We call this "static cling." Consider charged particles near a charged screen as shown in this animation. What happens to the positively charged particles? How about negatively charged particles? Now consider neutral particles as in this animation. What happens to the neutral particle between two charged screens? It gets polarized and then attracted to the screen. Notice that a charged screen can therefore attract both charged particles and neutral particles. This explains why your computer and television screens (which are charged) collect dust so easily.

Illustration authored by Anne J. Cox.
Script authored by Morten Brydensholt.
Applet authored by Vojko Valencic.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.