18.5 Electric field: concept of a field revisited

Learning objectives

By the end of this section, you will be able to:

• Describe a force field and calculate the strength of an electric field due to a point charge.
• Calculate the force exerted on a test charge by an electric field.
• Explain the relationship between electrical force ( F ) on a test charge and electrical field strength ( E ).

The information presented in this section supports the following AP® learning objectives and science practices:

• 2.C.1.1 The student is able to predict the direction and the magnitude of the force exerted on an object with an electric charge q placed in an electric field E using the mathematical model of the relation between an electric force and an electric field: $\overrightarrow{F}=q\overrightarrow{E}$ , a vector relation. (S.P. 2.2)
• 2.C.1.2 The student is able to calculate any one of the variables – electric force, electric charge, and electric field – at a point given the values and sign or direction of the other two quantities. (S.P. 2.2)
• 2.C.2.1 The student is able to qualitatively and semiquantitatively apply the vector relationship between the electric field and the net electric charge creating that field. (S.P. 2.2, 6.4)
• 3.C.4.1 The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces. (S.P. 6.1)
• 3.C.4.2 The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and that they therefore have certain directions. (S.P. 6.2)

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, $F=k\mathrm{|}{q}_1{q}_2\mathrm{|}/r^2$ , its magnitude is given by the equation $F=k\mathrm{|}\mathrm{qQ}\mathrm{|}/r^2$ , for a point charge    (a particle having a charge $Q$ ) acting on a test charge     $q$ at a distance $r$ (see [link] ). Both the magnitude and direction of the Coulomb force field depend on $Q$ and the test charge $q$ .