# 2Coordinate Systems

In this chapter we discuss three coordinate systems frequently encountered in electromagnetics: Cartesian, cylindrical, and spherical. In each system we define the relevant operations and properties. We conclude by showing the transformations between the systems. These transformations are necessary when deriving the radiation from a Hertzian dipole, as shown in the EMC applications section at the end of this chapter.

## 2.1 Cartesian Coordinate System

Cartesian coordinate system is shown in Figure 2.1.

Unit vectors in this system, denoted * a_{x}*,

*, and*

**a**_{y}*, are usually drawn at the origin (but can be drawn at any point in space). They point in the direction of the increasing coordinate variables, and are orthogonal to each other.*

**a**_{z}A point *P* can be represented as a triple of numbers

where *x*, *y*, and *z* are called the *coordinates* of *P*.

The *ranges* of the coordinate variables are

A *vector* **A** can be represented as a triple

where *A _{x}*,

*A*, and

_{y}*A*are called the

_{z}*components*of

*.*

**A**A vector **A** can be decomposed into a sum of three vectors along ...

Get *Foundations of Electromagnetic Compatibility with Practical Applications* now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.