محاضرة 2

In general, the physical quantities we shall be dealing with in EM are functions of space
and time. In order to describe the spatial variations of the quantities, we must be able to
define all points uniquely in space in a suitable manner. This requires using an appropriate
coordinate system.
A point or vector can be represented in any curvilinear coordinate system, which may
be orthogonal or nonorthogonal.
An orthogonal system is one in which the coordinates arc mutually perpendicular.
Nonorthogonal systems are hard to work with and they are of little or no practical use.
Examples of orthogonal coordinate systems include the Cartesian (or rectangular), the cir-
cular cylindrical, the spherical, the elliptic cylindrical, the parabolic cylindrical, the
conical, the prolate spheroidal, the oblate spheroidal, and the ellipsoidal.
1
A considerable
amount of work and time may be saved by choosing a coordinate system that best fits a
given problem. A hard problem in one coordi nate system may turn out to be easy in
another system.
In this text, we shall restrict ourselves to the three best-known coordinate systems: the
Cartesian, the circular cylindrical, and the spherical. Although we have considered the
Cartesian system in Chapter 1, we shall consider it in detail in this chapter. We should bear
in mind that the concepts covered in Chapter 1 and demonstrated in Cartesian coordinates
are equally applicable to other systems of coordinates. For example, the procedure for