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# Illustration 22.1: Charge and Coulomb's Law

x = | q = C

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 m, x = 0 m, and x = 1 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/r2).

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.

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