Chapter 23 The Electric Field

A photograph of lightning patterns in the sky.

Lightning, a vivid example of the power of electricity, occurs when the electric field between the ground and the clouds becomes too strong.

In This Chapter, you will learn how to calculate and use the electric field.

Where do electric fields come from?

Electric fields are created by charges.

  • Electric fields add. The field due to several point charges is the sum of the fields due to each charge.

  • Electric fields are vectors. Summing electric fields is vector addition.

  • Two equal but opposite charges form an electric dipole.

  • Electric fields can be represented by electric field vectors or electric field lines.

《 LOOKING BACK Section 22.5 The electric field of a point charge

The figure illustrates the field of a dipole.

What if the charge is continuous?

For macroscopic charged objects, like rods or disks, we can think of the charge as having a continuous distribution.

  • A charged object is characterized by its charge density—the charge per length, area, or volume.

  • We’ll divide objects into small point charge–like pieces ΔQ.

  • The summation of their electric fields will become an integral.

  • We’ll calculate the electric fields of charged rods, loops, disks, and planes.

The figure illustrates the charge distribution on a long rod.

What fields are especially important?

We will develop and use four important electric field models.

The figure contains four parts that illustrates the electric field models.

What is a parallel-plate capacitor?

Two parallel conducting plates with equal but opposite charges form a parallel-plate capacitor. You’ll learn that the electric field between the plates is a uniform electric field, the same at every point. Capacitors are also important elements of circuits, as you’ll see in Chapter 26.

The figure illustrates the charge distribution on a parallel plate capacitor.

How do charges respond to fields?

Electric fields exert forces on charges.

  • Charged particles accelerate. Acceleration depends on the charge-to-mass ratio.

  • A charged particle in a uniform field follows a parabolic trajectory.

  • A dipole in an electric field feels a torque that aligns the dipole with the field.

《 LOOKING BACK Section 4.2 Projectiles

The figure represents a dipole placed in a uniform electric field.

Learning Objectives

After studying this chapter, you should be able to

  1. 23.1 Calculate the electric fields of multiple point charges and electric dipoles.

  2. 23.2 Calculate the electric field of a continuous distribution of charge.

  3. 23.3 Work with the electric field of macroscopic charged objects.

  4. 23.4 Solve problems about parallel-plate capacitors and uniform electric fields.

  5. 23.5 Solve problems about charged particles moving in electric fields.

  6. 23.6 Calculate the torque on a dipole in an electric field.