Coaxial Cable – Mathematics Primer for Vector Fields

By Dr. Eugene Patronis

Dr. Patronis will be writing a series of articles on the properties of coaxial cable. This primer lays some mathematical ground work for the motivated learner.

This is the second in a series of articles dealing with coaxial cables operating in the frequency span from direct current through the microwave region. In order to make the ideas meaningful to the widest audience this article will be devoted to the mathematics necessary to properly describe physical variables that have a dimension or unit, a size or magnitude, and a direction in space.

For the moment we will be concerned with physical variables that fall into two distinctly different mathematical categories. The first category includes items such as mass, charge, density, pressure, and temperature among others. These are scalar quantities that may have a particular unit but otherwise have only a numerical value or magnitude and are subject to the rules of ordinary arithmetic and algebra. The second category includes items such as displacement, velocity, acceleration, force, etc. These are vector quantities that possess a particular unit, a scalar magnitude, and a direction in space as well. Scalar and vector physical variables both may be called field variables if they change as functions of position in space and possibly of time.