Application of Geometric Algebra to Electromagnetic Scattering by Andrew Seagar

Author:Andrew Seagar
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Clifford

Quaternion

a

A

b

B

c

C

d

D

Operator

0

0

k

0

0

0

0

Field

0

0

0

0

0

0

Source

0

0

0

0

0

0

Potential

0

0

0

0

0

0

For monochromatic fields , the complex signal can be eliminated and Maxwell’s equations can be written in terms the magnitude of phasors alone. This is achieved by expanding the product:

(5.20)

The number of variables is effectively reduced from three space and one time, to three space plus a fixed parameter, the wavenumber k. The complex signal can be eliminated from both sides.

Table 5.3 reproduces the electromagnetic quantities given in Table 5.2, converted from temporal to phasor form in the same way as for the field in Eq. 5.19. All quantities with a subscript k are the magnitudes of phasors, with the exception of the differential operator .

In the monochromatic frequency domain Maxwell’s equations are written in phasor form as:

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