The electromagnetic field
angular momentum of the electron



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




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








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




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





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:




Thecomponent of angular momentum density is:




As we know the volume element is:

For the  component of angular momentum density, because



Thus we can get the  component of angular momentum:



For the z component of electron angular momentum, we have














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


When , the z component of angular momentum is:




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:




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.






Combine (6.14) and (6.15), thus:




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:
















As we know, the vacuum impedance is:




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





Electromagnetic field angular momentum in condensed matter systems

Douglas Singleton, Jerzy Dryzek

Phys. Rev. B, 62, 13070 (2000)


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D. Singleton
Am. J. Phys. 66, 697 (1998)


A derivation of the classical monopole energy loss from angular momentum conservation

J. S. Trefil

Am. J. Phys. 51, 1113 (1983)


A Newton–Faraday approach to electromagnetic energy and angular momentum storage in an electromechanical system

N. Gauthier

Am. J. Phys. 70, 1034 (2002)


Field angular momentum in atomic sized systems

Jerzy Dryzek , Douglas Singleton

Am. J. Phys. 67, 930 (1999)


Electromagnetic momentum density and the Poynting vector in static fields
Francis S. Johnson, Bruce L. Cragin, and R. Richard Hodges

Am. J. Phys. 62, 33 (1994)


Dipoles at rest

David J. Griffiths 

Am. J. Phys. 60, 979 (1992)


Rotating waves

Peter H. Ceperley

Am. J. Phys. 60, 938 (1992)


Conservation of linear and angular momentum and the interaction of a moving charge with a magnetic dipole

V. Hnizdo

Am. J. Phys. 60, 242 (1992)


Electromagnetic angular momentum for a rotating charged shell

Antonio S. de Castro

Am. J. Phys. 59, 180 (1991)


Angular momentum of a charge–monopole pair

K. R. Brownstein

Am. J. Phys. 57, 420 (1989)


Angular momentum in the field of an electron

Jack Higbie

Am. J. Phys. 56, 378 (1988)


Angular momentum in static electric and magnetic fields: A simple case

H. S. T. Driver

Am. J. Phys. 55, 755 (1987)


What is spin?

Hans C. Ohanian

Am. J. Phys. 54, 500 (1986)


Electromagnetic angular momentum

Robert H. Romer

Am. J. Phys. 53, 15 (1985)


Field angular momentum of an electric charge interacting with a magnetic dipole

A. C. Lawson

Am. J. Phys. 50, 946 (1982)


Angular momentum of a static electromagnetic field

E. Corinaldesi

Am. J. Phys. 48, 83 (1980)


The Law of Conservation of Angular Momentum

Ph. M. Kanarev

Journal of Theoretics Vol.4-4


Model of the Electron

Ph. M. Kanarev

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





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