# Electric Charge and Electric Field

## Electric Field: Concept of a Field Revisited


### Learning Objectives

By the end of this section, you will be able to:
1. Describe a force field and calculate the strength of an electric field due to a point charge.
2. Calculate the force exerted on a test charge by an electric field.
3. Explain the relationship between electrical force (F) on a test charge and electrical field strength (E).
Contact forces, such as between a baseball and a bat, are explained on the small scale by the interaction of the charges in atoms and molecules in close proximity. They interact through forces that include the Coulomb force. Action at a distance is a force between objects that are not close enough for their atoms to “touch.” That is, they are separated by more than a few atomic diameters.
For example, a charged rubber comb attracts neutral bits of paper from a distance via the Coulomb force. It is very useful to think of an object being surrounded in space by a force field. The force field carries the force to another object (called a test object) some distance away.

### Concept of a Field

A field is a way of conceptualizing and mapping the force that surrounds any object and acts on another object at a distance without apparent physical connection. For example, the gravitational field surrounding the earth (and all other masses) represents the gravitational force that would be experienced if another mass were placed at a given point within the field.
In the same way, the Coulomb force field surrounding any charge extends throughout space. Using Coulomb’s law, , its magnitude is given by the equation

, for a point charge (a particle having a charge ) acting on a test charge  at a distance  (see ). Both the magnitude and direction of the Coulomb force field depend on  and the test charge .
To simplify things, we would prefer to have a field that depends only on  and not on the test charge . The electric field is defined in such a manner that it represents only the charge creating it and is unique at every point in space. Specifically, the electric field  is defined to be the ratio of the Coulomb force to the test charge:

where  is the electrostatic force (or Coulomb force) exerted on a positive test charge
. It is understood that
 is in the same direction as
. It is also assumed that  is so small that it does not alter the charge distribution creating the electric field. The units of electric field are newtons per coulomb (N/C). If the electric field is known, then the electrostatic force on any charge  is simply obtained by multiplying charge times electric field, or 
        
          . Consider the electric field due to a point charge . According to Coulomb’s law, the force it exerts on a test charge

 is

. Thus the magnitude of the electric field,
, for a point charge is
Since the test charge cancels, we see that
The electric field is thus seen to depend only on the charge  and the distance ; it is completely independent of the test charge .

### Test Prep for AP Courses


### Section Summary

1. The electrostatic force field surrounding a charged object extends out into space in all directions.
2. The electrostatic force exerted by a point charge on a test charge at a distance  depends on the charge of both charges, as well as the distance between the two.
3. The electric field  is defined to be
    where 
4. The magnitude of the electric field  created by a point charge  is
    where 

### Conceptual Questions


### Problem Exercises
