The mass of the electron as an electromagnetic effect

by David Jonsson, Uppsala , Sweden


Take a look at the equation for the magnetic flux around a moving electron in the
nonrelativistic case, the simple Biot-Savarts law

            _   _
_   mu0 e   v x r
B = ----- . -----   (1)
    4 Pi       3
              r

The energy-density of this field is according to eq. (2)

      _ 2
      B       _2  _   _
u = -----  , (B = B * B)   (2)
    2 mu0


In order to calculate the magnetic energy of the moving electron we insert (1)
into (2) to get (3)

         2    2    2 
    mu0 e    v  sin (theta)
u = ------ . -------------   (3)
         2         4
    32 Pi         r


Lets integrate eq. (3) outside the electron to find out the entire energy of its
magnetic field.

         2    2 
    mu0 e    v
U = ------ . --   (4)
             r
    12 Pi     e
    

Lets install the classical electron radius re,

                 2                 2
                e             mu0 e
r   = ------------------- = --------  (5)
 e                   2       4 Pi m
      4 Pi epsilon0 c  m           e
                        e

in (4) to get

         2
     m  v
      e
U= -------
      3

This reminds very much of the equation of the kinetic energy of the electron.
Only 1/6 of the kinetic energy is missing but remember that I havenŐt included the
field inside the electron in the calculus.  Can it be so simple that the inertia
of the electron is due to LenzŐ law only?