Chapter 6

As we know, the electromagnetic field has the properties of energy, momentum and angular momentum. The electromagnetic field momentum density is: (6.1)

Based upon the electromagnetic field momentum, and then we can define the field angular momentum density as follows: (6.2)

Thus: (6.3)

Then integrating equation (6.3), we can get the field angular momentum: (6.4)

Combine the equation (4.2) and (5.2) into equation (6.3),

Thus: (6.5)

For the cylindrical coordinate ( , , z), which has the follows relationship with the spherical coordinate (r, , ):  We can separate the angular momentum density into the z component and component,

The z component of angular momentum density is: (6.6)

The component of angular momentum density is: (6.7)

As we know the volume element is: For the component of angular momentum density, because (6.8)

Thus we can get the component of angular momentum: For the z component of electron angular momentum, we have (6.9)

Thus: (6.10) (6.11)

Therefore: (6.12)

The equation (6.12) is the angular momentum distribution equation of an electron.

When , the z component of angular momentum is: (6.13)

The equation (6.13) is the angular momentum within the sphere of radius r of an electron.

The angular momentum distribution is a kind of cumulative gamma distribution in mathematics [B]

When thus: (6.14)

The above angular momentum is the electron’s electromagnetic field angular momentum in total.

What is the electron spin? As we know, the electron spin is the electron intrinsic angular momentum. Let us make an assumption that electron spin is the electromagnetic field angular momentum, which also means that the electron spin is of purely electromagnetic origin.

Thus: (6.15)

Combine (6.14) and (6.15), thus: (6.16)

From equation (6.16), we found out that the multiple of electric charge unit ‘e’ and magnetic charge unit ‘g’ equal the Planck’s constant ‘h.

Then, we can also calculate the ratio of magnetic charge ‘g’ and electric charge ‘e’ as follows: (6.17)

Thus: (6.18)

So: (6.19)

Thus: (6.20)

As we know, the vacuum impedance is: (6.21)

So we can see the ratio of magnetic charge unit ‘g’ and electric charge unit ‘e’ has the unit of impedance.

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APEIRON Vol. 7 Nr. 3-4, July-October, 2000