Chapter 14

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)