Page 22 - Engineering Electromagnetics, 8th Edition

4 ENGINEERING ELECTROMAGNETICS

to use only the three simple methods, and the simplest of these is the rectangular,or
rectangular cartesian, coordinate system.
In the rectangular coordinate system we set up three coordinate axes mutually
at right angles to each other and call them the x, y, and z axes. It is customary to
choose a right-handed coordinate system, in which a rotation (through the smaller
angle) of the x axis into the y axis would cause a right-handed screw to progress in
the direction of the z axis. If the right hand is used, then the thumb, forefinger, and
middle finger may be identified, respectively, as the x, y, and z axes. Figure 1.2a
shows a right-handed rectangular coordinate system.
A point is located by giving its x, y, and z coordinates. These are, respectively,
the distances from the origin to the intersection of perpendicular lines dropped from
the point to the x, y, and z axes. An alternative method of interpreting coordinate

Figure 1.2 (a)A right-handed rectangular coordinate system. If the curved fingers of the
right hand indicate the direction through which the x axis is turned into coincidence with the
y axis, the thumb shows the direction of the z axis. (b) The location of points P(1, 2, 3) and
Q(2, −2, 1). (c) The differential volume element in rectangular coordinates; dx, dy, and dz
are, in general, independent differentials.