Definitions of electric fields and potentials
From Physics 231 and from the previous lecture you should be comfortable with the concepts of force and potential energy. In Physics 231, you used the equation:
where 
is
the potential energy added to an object by a force 
pushing it a distance 
. Only the component of force acting
parallel to the displacement changes the potential energy;
hence the 
factor.
Since all electric forces and potentials are proportional to the charge of an object, it is convenient to define an electric field and electric potential, which are the electric force and the electric potential energy of an object divided by the charge of that object.
The electric field is a vector (it points in the direction of the force that would apply to a positive charge placed in the field) while the electric potential is a scalar (it has no direction).
The electric field and electric potential generated by a point charge are
