2) Electromagnetic calculation. [ Return home ]

As derived with the Maxwell equation (Poynting's theorem), the electric and magnetic energy densities are and

For the electromagnetic field of an electron in uniform motion, it has been derived by me and by Lorentz with the Maxwell equations(see R. Beckers, Théorie des électrons, Librairie félix Alcan, Paris, (1938), pp.50-58 ) that the fields of a non spinning electron are:

and

The result is a whole energy density: of:

The integration of the energy density will be done outside the contracted ellipsoidal nucleus of frozen ether whose radius is ro at rest. The fact that ro remains the greatest axis of the ellipsoidal nucleus (while in motion) will be justified in the ending discussion.

With the energy is:

By a Jacobi transformation , y=y' and z=z' with ,

this integral becomes with x',y',z' renamed x,y,z:

This time, due to the change of variable, the mathematical nucleus is spherical.

If we note that: , valid also for y and z, and that:, we have finally:

The mass will be defined in the hypersonic calculation with an equivalence here which is:

leading obviously to

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