Chapter 4: Gradient and Dipole

POTENTIAL GRADIENT
We now have two methods of determining potential, one directly from the electric field intensity by means of a line integral, and another from the basic charge distribution itself by a volume integral. Neither method is very helpful in determining the fields
in most practical problems, however, for as we will see later, neither the electric field intensity nor the charge distribution is very often known. Preliminary information is much more apt to consist of a description of two equipotential surfaces, such as the
statement that we have two parallel conductors of circular cross section at potentials of 100 and ?100 V. Perhaps we wish to find the capacitance between the conductors, or the charge and current distribution on the conductors from which losses may be calculated.
These quantities may be easily obtained from the potential field, and our immediate goal will be a simple method of finding the electric field intensity from the potential.

THE ELECTRIC DIPOLE
The dipole fields that we develop in this section are quite important because they form the basis for the behavior of dielectric materials in electric fields, as well as justifying the use of images, Moreover, this development will serve to illustrate the importance of the potential concept presented in this chapter.
An electric dipole, or simply a dipole, is the name given to two point charges of equal magnitude and opposite sign, separated by a distance that is small compared to the distance to the point P at which we want to know the electric and potential fields.