Chapter
14

The electromagnetic field equation in complex form



The electric field and magnetic field can be expressed in complex form.

 

Let us define the electromagnetic charge density in complex form as:

 

(14.1)

 

The Electromagnetic field strength in complex form as:

 

(14.2)

 

And also:

 

(14.3)

 

As we know the electromagnetic field energy density is:

 

(14.4)

 

Thus, we have:

 

(14.5)

 

The electromagnetic field momentum density is:

 

(14.6)

 

Thus, we have:

 

(14.7)

 

Then we can rewrite the electromagnetic field equation as follows:


(14.8)


(14.9)

 

(14.10)

 

The equation (14.10) can be called the hydro-electromagnetic equation.

 

As we know:

(14.11)

 

Thus:

(14.12)

 

Thus the hydro-electromagnetic equation can be rewritten in the complex form as:

 

(14.13)

 

And thus, we can rewrite the equation (14.13) as follows:

 

(14.14)

 

Then the hydroelectric equation can be rewritten as:

 

(14.15)

 

Then the hydromagnetic equation can be rewritten as:

 

(14.16)

 

For the electron, we have

 

(14.17)

 

And

 

(14.18)

 

As we know:

 

(14.19)

 

Thus:

 

(14.20)

 

Let us define:

(14.21)

 

Thus:

 

(14.22)

 

So:

 

(14.23)

 

Let us define:


(14.24)

 

As we know:

 

(14.25)

 

(14.26)

 

Thus:

 

(14.27)

 

(14.28)

 

(14.29)

 

Thus:

 

(14.30)

 

Thus:

 

(14.31)

 

 


What is the electron spin?
ISBN 0-9743974-9-0
Copyright 2003
Gengyun Li
All rights reserved
http://www.electronspin.org