Chapter 23: Electric Fields

Learning Goals

  1. Become familiar with the basic properties of electric charge, insulators and conductors.
  2. Be able to apply Coulomb's law for electrostatic force.
  3. Understand the concept and definition of electric field.
  4. Solve electric field and electric force problems involving discrete and continuous charge distributions.
  5. Understand electric field lines.

 

Electric Charge

Electric charge has certain fundamental properties that you should consider each time you solve a problem:
  1. Two kinds of charge: + and –
  2. The electric between two point charges always acts along the line connecting the two charges.
  3. Like charges repel, unlike charges attract
  4. Electric charge is always conserved in any physical process
  5. The SI unit of electric charge is the Coulomb (C)
  6. Electric charge is quantized in units of e = 1.602 x 10-19C

 

Coulomb’s Law

Coulomb’s law describes the vector magnitude (which is always positive) of the electric force between two point charges:

Coulomb's Law

where the constant k is given by
k = 8.9875 x 109 Nm2/C2

Items 2 and 3 above along with Coulomb’s law can be used to construct a vector diagram of any number of electric forces acting on a given charge.

 

Electric Field

The electric field at a point in space is defined as the force per unit charge acting on a small positive test charge q0 placed at that position:

Efield Definition

The SI units of electric field are N/C.

For a point charge, Coulomb’s law may be used to find the magnitude of electric field:

Efield: point charge

It is important to remember that electric field, like force is a vector. The electric force on the small positive test charge q0 used to define the field, along with items 2 and 3 above are used to construct the appropriate vector diagram for any given situation.

 

Continuous Charge Distributions

If many charges are distributed in space in a continuous distribution, then one approach is to treat infinitesimal charge elements as point charges, and use Coulomb’s law to find the corresponding infinitesimal vector element of electric field:

Integral formula - Coulomb form

This equation is really shorthand for up to three different integrals which sum the components of the vector integrand along individual coordinate directions. It is often possible (and important) to utilize symmetry arguments to determine which of these integrals are nonzero without explicitly performing the integration.

The Coulomb approach outlined here is not the only way to determine electric fields due to extended continuous charge distributions. In later chapters, you will learn about two more techniques which are often easier to implement: Gauss’s law and electric potential.