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25 - Electric Potential - Chapter 25 Electric Potential...

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Electric Potential CHAPTE R OUTLI N E 25.1 Potential Difference and Electric Potential 25.2 Potential Differences in a Uniform Electric Field 25.3 Electric Potential and Potential Energy Due to Point Charges 25.4 Obtaining the Value of the Electric Field from the Electric Potential 25.5 Electric Potential Due to Continuous Charge Distributions 25.6 Electric Potential Due to a Charged Conductor 25.7 The Millikan Oil-Drop Experiment 25.8 Applications of Electrostatics Processes occurring during thunderstorms cause large differences in electric potential between a thundercloud and the ground. The result of this potential difference is an electrical discharge that we call lightning, such as this display over Tucson, Arizona. (© Keith Kent/ Photo Researchers, Inc.) Chapter 25 762
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763 T he concept of potential energy was introduced in Chapter 8 in connection with such conservative forces as the gravitational force and the elastic force exerted by a spring. By using the law of conservation of energy, we were able to avoid working directly with forces when solving various problems in mechanics. The concept of potential energy is also of great value in the study of electricity. Because the electrostatic force is conserva- tive, electrostatic phenomena can be conveniently described in terms of an electric potential energy. This idea enables us to define a scalar quantity known as electric potential. Because the electric potential at any point in an electric field is a scalar quantity, we can use it to describe electrostatic phenomena more simply than if we were to rely only on the electric field and electric forces. The concept of electric potential is of great practical value in the operation of electric circuits and devices we will study in later chapters. 25.1 Potential Difference and Electric Potential When a test charge q 0 is placed in an electric field E created by some source charge distribution, the electric force acting on the test charge is q 0 E . The force q 0 E is conservative because the force between charges described by Coulomb’s law is conserv- ative. When the test charge is moved in the field by some external agent, the work done by the field on the charge is equal to the negative of the work done by the exter- nal agent causing the displacement. This is analogous to the situation of lifting an object with mass in a gravitational field—the work done by the external agent is mgh and the work done by the gravitational force is mgh . When analyzing electric and magnetic fields, it is common practice to use the notation d s to represent an infinitesimal displacement vector that is oriented tangent to a path through space. This path may be straight or curved, and an integral performed along this path is called either a path integral or a line integral (the two terms are synonymous).
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