Chapter
15

The conservation of energy

 

 

The conservation of energy is one of the most basic physics laws, for the electromagnetic field, the energy conservation equation is as follows:

 

                                                                                                   (15.1)

 

In which  is the mass density,  is the field velocity.

The mass density and energy density have the following relationship:

 

 

In which u is the electromagnetic field energy density.

 

From equation (14.15) and (14.16), we have:

 

                                                                      (15.2)

 

And

 

                                                                   (15.3)

 

Thus:

 

                                                (15.4)

 

And

 

                                          (15.5)

 

Thus:

 

                                               (15.6)

 

And

 

                                           (15.7)

 

Combine (15.6) and (15.7), thus:

 

                            (15.8)

 

Let us assume that the electromagnetic energy is conserved, therefore, we have:

 

                                                                                                   (15.9)

 

Thus:

 

                                                                                   (15.10)

 

Thus, we have:

 

                                                        (15.11)

 

As we know:

 

                                                                                                          (15.12)

 

                                                                                                        (15.13)

 

Let us define:

 

                                                                                                                (15.14)

 

                                                                                                              (15.15)

 

From the electromagnetic field energy conservation equation, then we can get the following equation:

 

                                                 (15.16)

 

Then we can rewrite the electromagnetic field as follows:


                                                                                                            (15.17)

 

                                                                                                            (15.18)

 

                                                                                  (15.19)

 

                                                                    (15.20)

 

                                                                 (15.21)

 

                                                    (15.22)

 

 


What is the electron spin?
ISBN 0-9743974-9-0
Copyright © 2003
Gengyun Li
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