Chapter 26 Potential and Field

A photograph of rows of solar panels.

These solar cells are photovoltaic cells, meaning that light creates a voltage—a potential difference.

In This Chapter, you will learn how the electric potential is related to the electric field.

How are electric potential and field related?

The electric field and the electric potential are intimately connected. In fact, they are simply two different perspectives on how source charges alter the space around them.

  • The electric potential can be found if you know the electric field.

  • The electric field can be found if you know the electric potential.

  • Electric field lines are always perpendicular to equipotential surfaces.

  • The electric field points “downhill” in the direction of decreasing potential.

  • The electric field is stronger where equipotentials are closer together.

《 LOOKING BACK Sections 25.4, 25.5, and 25.6 The electric potential and its graphical representations

The figure consists of two parts that illustrate the electric field and electric potential around a positive charge.

What are the properties of conductors?

You’ll learn about the properties of conductors in electrostatic equilibrium, finding the same results as using Gauss’s law:

  • Any excess charge is on the surface.

  • The interior electric field is zero.

  • The exterior electric field is perpendicular to the surface.

  • The entire conductor is an equipotential.

The figure illustrates the electric field due to a charged conductor.

What are sources of electric potential?

A potential difference—voltage—is created by separating positive and negative charges.

  • Work must be done to separate charges. The work done per charge is called the emf of a device. Emf is measured in volts.

  • We’ll use a charge escalator model of a battery in which chemical reactions “lift” charges from one terminal to the other.

    The figure illustrates a charge escalator model of a battery.

What is a capacitor?

The figure illustrates a parallel-plate capacitor.

Any two electrodes with equal and opposite charges form a capacitor. Their capacitance indicates their capacity for storing charge. The energy stored in a capacitor will lead us to recognize that electric energy is stored in the electric field.

《 LOOKING BACK Section 23.5 Parallel-plate capacitors

How are capacitors used?

The figure illustrates a circuit diagram of three capacitors connected in parallel.

Capacitors are important circuit elements that store charge and energy.

  • You’ll learn to work with combinations of capacitors arranged in series and parallel.

  • You’ll learn that an insulator—called a dielectric—between the capacitor plates alters the capacitor in useful ways.

Learning Objectives

After studying this chapter, you should be able to

  1. 26.1 Explain the connection between electric potential and field.

  2. 26.2 Calculate the electric field from its potential.

  3. 26.3 Illustrate the geometry of potential and field.

  4. 26.4 Solve problems about the potential of a conductor in electrostatic equilibrium.

  5. 26.5 Work with the emf of sources of potential.

  6. 26.6 Solve problems about capacitors and capacitance.

  7. 26.7 Calculate the equivalent capacitance of a combination of capacitors.

  8. 26.8 Calculate the energy stored in a capacitor.

  9. 26.9 Determine electric fields and potentials in a dielectric.