Chapter Review
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Chapter 19: Electric Charges, Forces, and Fields Chapter Review |
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Chapter Review
This chapter begins our study of electricity and magnetism. Electric and magnetic forces are due to a phenomenon that we have not studied in previous chapters, namely, electric charge. The existence of electric charge and its consequences creates a completely new branch of physics that adds to the concepts and phenomena that we studied in previous chapters.
19-1 - 19-2 Electric Charge, Insulators, and Conductors
Through a series of experiments over many years we have now come to understand that we are all made up of smaller objects (atoms) that contain electric charge. To the best of our present knowledge, electric charge is a fundamental property of nature that comes in two types called positive charge and negative charge. Most bulk materials contain an equal number of positive and negative charges and are said to be electrically neutral (or to have zero net charge).
Atoms consist of a small central nucleus that contains positively charged particles called protons. The nucleus is surrounded by an equal number of negatively charged particles called electrons. The electric charge of protons and electrons have the same magnitude
e = 1.60 x 10-19 C.
An electron has charge of -e and protons carry a charge of +e. The SI unit of electron charge is called the coulomb (C); this is a new unit that is not derived from just [L], [M], and [T]. However, the coulomb is officially considered to be a derived unit; we will see from what it is derived in a later chapter. For now we will denote the dimension associated with electric charge as [C].
One of the properties of electric charge is that it is quantized. This fact means that the charge only comes in discrete units. The smallest available charge is that of a proton or electron, e. Another property of electric charge is that it is conserved. Therefore, in any physical process electric charge is never created or destroyed; the total electric charge of the universe remains constant.
The positive and negative charges in an object can become separated, usually by the movement of electrons, so that one side of the object contains more of the negative charge and the other side is left with more of the positive charge. Such objects are said to be polarized. In atoms (and molecules - bound groups of atoms) electrons can be completely removed or extra electrons can be added. An atom with one or more electrons removed will have a net positive charge and is called a positive ion; an atom with extra electrons will have a negative charge and is called a negative ion.
Important to our ability to make practical use of electricity is the fact that in some materials, called conductors, electrons are relatively free to move, while in other materials, called insulators, electrons are not very free to move. Metals are typically good conductors of electricity. Examples of commonly used insulators are rubber, plastic, and wood. There are also materials, called semiconductors, whose behavior is not clearly conducting or insulating. These materials can be manipulated to be more conducting in some situations and more insulating in others. The ability to manipulate semiconductors to control the flow of electricity has been a major triumph of modern technology.
Practice Quiz
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Physlet Illustration: Electric Charges | |
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| In this simulation, four charged particles are shown, along with a vector representing the net electric force experienced by each charge. Charge 1 has a value of +2 mC. What are the signs of the other charges? | |
Hints:
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19-3 Coulomb's Law
Electric charges exert forces on each other. The rule for determining this force is called Coulomb's law. This law states that for two stationary point charges of magnitudes q1 and q2, the magnitude of the electrostatic force between them is proportional to the product 
and inversely proportional to the square of the distance r between them. Therefore, the magnitude of the force is given by
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where k is a proportionality that has the value
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Two additional rules allow us to determine the direction of the force. One rule is that the force is directed along the line joining the charges. The second rule is that like charges repel each other and opposite charges attract each other. Note that there are actually two forces, one exerted on q1 by q2 (F12) and one exerted on q2 by q1 (F21). These forces have equal magnitudes, given by F above, and point in opposite directions in accordance with Newton's law of action and reaction. When more than two charges are involved, the force on any one charge can be determined using the principle of superposition. This principle states that the force on any charge is the vector sum of the forces that each of the other charges exert on it individually.
In addition to having individual point charges it is also common to deal with continuous distributions of charge. An interesting example is that of an amount of charge Q distributed uniformly over the surface of a sphere. The force experienced by a point charge q outside the sphere works out, by superposition, to look just like Coulomb's law
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where r, in this case, is the distance of q from the center of the sphere. When dealing with continuous distributions of charge it is often convenient to work with charge densities. In this case at hand we have a surface charge density, 
, which is the charge per area ( = Q/A) over the sphere. So, for an amount of charge Q spread over the surface of a sphere of radius R the surface charge density is given by
and has SI units of C/m2.
Physlet Illustration: Coulomb's Law | |
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| In this simulation, two charged particles are shown, along with vectors representing the net electric force experienced by each charge. Q1 is located at the point (0,0), and has a charge of 0.1 mC. Distances are given in cm and the force in Newtons. Can you verify Coulomb's law of electric force? | |
Hints:
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Example 19.1 Coulomb's law and Superposition: Given a configuration of three charged particles such that charge q1 = 5.3 nC has (x, y) coordinates of (1.5 m, 0.0 m), charge q2 = 9.2 nC is located at (0.0 m, 2.0 m), and charge q3 = -2.4 nC is located at the origin, determine the net force on charge q3.
Picture the Problem The picture shows the charge configuration of q1, q2, and q3.
Strategy Our basic strategy, in keeping with the principle of superposition, is to determine the force on q3 due to q1 and q2 separately using Coulomb's law, then get the net force on q3 as the vector sum of the two.
Solution
| 1. From the given coordinates, the distance between q1 and q3 is: | r13 = 1.5 m |
| 2. Using Coulomb's law, the magnitude of the force on q3 due to q1 is: |  |
| 3. Since the charges have opposite sign F31 must point toward q1: |  |
| 4. From the given coordinates, the distance between q2 and q3 is: | r23 = 2.0 m |
| 5. Using Coulomb's law, the magnitude of the force on q3 due to q2 is: |  |
| 6. Since the charges have opposite sign F31 must point toward q2: |  |
| 7. The net force on q3 is the sum of the two forces: |  |
Insight Notice that because q3 is a negative charge, I used the absolute value of the product of the charges in each application of Coulomb's law.
Physlet Illustration: Electric Charge and Forces | |
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| In this simulation, two spheres, are fixed at (-4, 0) and (+4, 0). Sphere 1 has a charge of -4 mC. Using the positive test charge, which is dragable, determine the charge on the second sphere. | |
Hints:
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Practice Quiz
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