Chapter 23 Electric Potential

Goals for Chapter 23 To study and calculate electrical potential energy To define and study examples of electric potential To trace regions of equal potential as equipotential surfaces To find the electric field from electrical potential

Introduction Electrical potential is sometimes modeled as a river. The width of the river defines how much water will be able to flow through its banks. The arc welder in the picture at right is taking advantage of a potential between the welding rod and material to be joined. The arc of electrical flow is so hot that the metals and the rod actually melt into one material.

Work, energy, and the path from start to finish The work done raising a basketball against gravity depends only on the potential energy, how high the ball goes. It does not depend on other motions. A point charge moving in a field exhibits similar behavior. Refer to Figures 23.1 and 23.2 below.

An electric charge moving in an electric field

A test charge will move with respect to other charges A test charge will move directly away from a like charge q.

The work done moving a test charge As a test charge moves away from a charge of like sign, the path does not matter (with respect to work or energy), only the distance between the charges.

Potential energy curves—PE versus r Graphically, the potential energy between like charges increases sharply to positive (repulsive) values as the charges become close. Unlike charges have potential energy becoming sharply negative as they become close (attractive). Refer to Example 23.1.

Electrical potential and multiple point charges The potential between multiple charges is done by vector addition of the individual energies as shown in Figure 23.8. Figure 23.9 shows this principle is applied to an ion engine for spaceflight. Refer to Example 23.2.

The electrical potential The potential of a battery can be measured between point a and point b (the positive and negative terminals). Moving with the electrical field decreases the electrical potential. Moving against the field lowers it.

A particle accelerator imparts amazingly large energies A particle accelerator can bring a charged particle to motion at velocities great enough to impart millions, even billions, of eV as kinetic energy. Figure 23.13 at right shows a particle accelerator at the Fermi Lab in Illinois. Refer to Example 23.3.

Finding the potential Refer to Example 23.4—multiple charges. This example is illustrated by Figure 23.14. Refer to Example 23.5—potential and potential energy. Refer to Example 23.6—potential by integration. This example is illustrated by Figure 23.15. Refer to Example 23.7—potential by integration. This example is illustrated by Figure 23.16.

Calculation of electrical potential Consider Problem-Solving Strategy 23.1. Refer to Example 23.8 with Figure 23.17.

Example—oppositely charged parallel plates Refer to Example 23.9 using Figure 23.19.

Example—a charged, conducting cylinder Refer to Example 23.10 using Figure 23.20.

Example—a ring of charge Refer to Example 23.11 using Figure 23.21.

Example—a line of charge Refer to Example 23.12 using Figure 23.22.

Equipotential surfaces and field lines Surfaces of equal potential may be drawn any charge or charges and the field lines they create.

Field lines and a conducting surface Refer to Figure 23.25 to illustrate the concept of field lines near a conducting surface.

The surface and interior of a conductor

Potential and fields of charge Follow Example 23.13 to calculate the potential and field of a point charge. Follow Example 23.14 to calculate the potential and field of a ring of charge.