From Fundamentals of Electromagnetic Fields
1.5 SPHERICAL COORDINATE SYSTEM
The way we have developed a cylindrical coordinate system, we now intend to develop a spherical coordinate system with reference to the Cartesian coordinate system. In a three-dimensional Cartesian coordinate system, we represent a point, say, P( x 1, y 1, z 1) as shown in Fig. 1 15. To locate this point, one has to travel a distance x 1 along the x-axis, y 1 parallel to the y-axis and z 1 parallel to the z-axis. The other way around, if we consider a plane x= x 1, y=y 1, and z=z 1 , then the intersection of these three planes is the point P( x 1, y 1, z 1) in space. The spherical coordinate system is a coordinate system derived in three dimensions where the required point is at a distance r 1 from the origin. The position vector of this space point makes an angle ? 1 with the z-axis and the position vector of the projected point (in the XY-plane) makes an angle 
with the x-axis. The meaning of 
is invariant here with reference the one in cylindrical coordinates. In other words, the required point is the intersection of three surfaces: Surface 1, which is the locus of all points at a constant distance from the origin i.e., a sphere of radius r 1 with the center...
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1.6 DIFFERENTIATION OF A VECTOR FIELD Let R (u) be a vector depending upon a scalar variable u=u(x,y,z). Then, where D u represents increments in u. The ordinary derivative of the vector R (u) with...
2.4 The Coordinate Systems Up to this point we have kept our discussion quite general and used graphical representations when manipulating vectors. From a mathematical point of view it is very...
1.3 POLAR COORDINATE SYSTEM Using a two-dimensional Cartesian coordinate system, we represent a point, say, A( x 1, y 1) as shown in Fig. 1 6. To locate this point, one has to travel the distance x 1...
3.1 TERMINOLOGY AND CONVENTIONS The standard IEEE terminology for antennas has been followed throughout this book with few exceptions. Detailed definitions and test procedures may be found in Ref. 1.
1.2 SCALARS AND VECTORS As stated in the introduction, the term scalar refers to the class of quantities that can be represented by a single real number, either positive or negative. On the other...
