19.1

Potential Energy

In Chapter 18 we discussed the electrostatic force that two point charges exert on each other, the magnitude of which is . The form of this equation is similar to that for the gravitational force that two particles exert on each other, which is , according to Newton’s law of universal gravitation (see Section 4.7). Both of these forces are conservative and, as Section 6.4 explains, a potential energy can be associated with a conservative force. Thus, an electric potential energy exists that is analogous to the gravitational potential energy. To set the stage for a discussion of the electric potential energy, let’s review some of the important aspects of the gravitational counterpart.
Figure 19-1, which is essentially Figure 6.10, shows a basketball of mass m falling from point A to point B. The gravitational force, , is the only force acting on the ball, where g is the magnitude of the acceleration due to gravity. As Section 6.3 discusses, the work WAB done by the gravitational force when the ball falls from a height of hA to a height of hB is

| (6.4)

Recall that the quantity mgh is the gravitational potential energy* of the ball, GPE = mgh (Equation 6.5), and represents the energy that the ball has by virtue of its position relative to the surface of the earth. Thus, the work done by the gravitational force equals the initial gravitational potential energy minus the final gravitational potential energy.

Figure 19-1 Gravity exerts a force, , on the basketball of mass m. Work is done by the gravitational force as the ball falls from A to B.

Figure 19-2 clarifies the analogy between electric and gravitational potential energies. In this drawing a positive test charge +q0 is situated at point A between two oppositely charged plates. Because of the charges on the plates, an electric field exists in the region between the plates. Consequently, the test charge experiences an electric force, (Equation 18.2), that is directed downward, toward the lower plate. (The gravitational force is being neglected here.) As the charge moves from A to B, work is done by this force, in a fashion analogous to the work done by the gravitational force in Figure 19-1. The work WAB done by the electric force equals the difference between the electric potential energy EPE at A and that at B:

| (19.1)

This expression is similar to Equation 6.4. The path along which the test charge moves from A to B is of no consequence because the electric force is a conservative force, and so the work WAB is the same for all paths (see Section 6.4).

Figure 19-2 Because of the electric field , an electric force, , is exerted on a positive test charge +q0. Work is done by the force as the charge moves from A to B.

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