The Electric Field

The definition of the electric field is directly analogous to, and has the same motivation as, the definition of the gravitational field:

Definition of the electric field

The electric field vector, E, at any location in space is found by placing a test charge qt at that point. The electric field vector is then given by E=F/qt, where F is the electric force on the test charge.

Charges are what create electric fields. Unlike gravity, which is always attractive, electricity displays both attraction and repulsion. A positive charge is a source of electric fields, and a negative one is a sink.

The most difficult point about the definition of the electric field is that the force on a negative charge is in the opposite direction compared to the field. This follows from the definition, since dividing a vector by a negative number reverses its direction. It is as though we had some objects that fell upward instead of down.

Self-Check	Find an equation for the magnitude of the field of a single point charge Q.
Answer	The reasoning is exactly analogous to that used in the previous section to derive an equation for the gravitational field of the Earth. The magnitude of the field is |F|/qt = |kQqt/r2|/qt = k|Q|/r2.

Superposition of electric fields