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Chapter 19 | Electric Potential and Electric Field 833
19.1 Electric Potential Energy: Potential Difference
Learning Objectives
By the end of this section you will be able to:
• Define electric potential and electric potential energy.
• Describe the relationship between potential difference and electrical potential energy.
• Explain electron volt and its usage in submicroscopic processes.
• Determine electric potential energy given potential difference and amount of charge.
The information presented in this section supports the following AP® learning objectives and science practices:
• 2.C.1.1 The student is able to predict the direction and the magnitude of the force exerted on an object with an electric charge q placed in an electric field E using the mathematical model of the relation between an electric force and an electric field: F = qE; a vector relation. (S.P. 6.4, 7.2)
• 2.C.1.2 The student is able to calculate any one of the variables—electric force, electric charge, and electric field—at a point given the values and sign or direction of the other two quantities. (S.P. 2.2)
• 5.B.2.1 The student is able to calculate the expected behavior of a system using the object model (i.e., by ignoring changes in internal structure) to analyze a situation. Then, when the model fails, the student can justify the use of conservation of energy principles to calculate the change in internal energy due to changes in internal structure because the object is actually a system. (S.P. 1.4, 2.1)
• 5.B.3.1 The student is able to describe and make qualitative and/or quantitative predictions about everyday examples of systems with internal potential energy. (S.P. 2.2, 6.4, 7.2)
• 5.B.3.2 The student is able to make quantitative calculations of the internal potential energy of a system from a description or diagram of that system. (S.P. 1.4, 2.2)
• 5.B.3.3 The student is able to apply mathematical reasoning to create a description of the internal potential energy of a system from a description or diagram of the objects and interactions in that system. (S.P. 1.4, 2.2)
• 5.B.4.1 The student is able to describe and make predictions about the internal energy of systems. (S.P. 6.4, 7.2)
• 5.B.4.2 The student is able to calculate changes in kinetic energy and potential energy of a system, using information
from representations of that system. (S.P. 1.4, 2.1, 2.2)
When a free positive charge is accelerated by an electric field, such as shown in Figure 19.2, it is given kinetic energy. The process is analogous to an object being accelerated by a gravitational field. It is as if the charge is going down an electrical hill
where its electric potential energy is converted to kinetic energy. Let us explore the work done on a charge by the electric field in this process, so that we may develop a definition of electric potential energy.
Figure 19.2 A charge accelerated by an electric field is analogous to a mass going down a hill. In both cases potential energy is converted to another form. Work is done by a force, but since this force is conservative, we can write .
The electrostatic or Coulomb force is conservative, which means that the work done on is independent of the path taken. This
is exactly analogous to the gravitational force in the absence of dissipative forces such as friction. When a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly.
We use the letters PE to denote electric potential energy, which has units of joules (J). The change in potential energy, , is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, . For example, work done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative . There must be a minus sign in front of to make positive. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point.