71078

Vector quantities

When we come to the representation of a sinusoidally varying vector quantity, we use as is common bold face characters to represent vectors. It is traditional to represent electromagnetic field quantities by upper case letters. If we are to distinguish clearly in our notation between the real time-varying variables and the time invariant complex

phasors which in the particular case of sinusoidal time variation may be used to represent

physical quantities, we are in nced of two bold face upper case character sets of

diffcrcnt

appearance.

This need is satisfied by the use of so called calligraphic characters, for example E. D.

H, and B, for the time-varying vectors directly representing time-varying physical vector

quantitics, and upright Roman letters, such as E. D. H, and B, for the time invariant complex vectors which can be used to represent sinusoidally varying vector quantitics.

In both cases the term vector indicates that the physical quantity has in the thrce dimensional space in which we live threc Cartesian components, each of which is a scalar

quantity, and each of which may have any of: no time variation, a generał non-sinusoidal

time variation, or perhaps a sinusoidal variation. In all three cases representation by the

calligraphic letters is appropriatc. but only in the last case is representation in the phasor

notation also appropriatc.