4.2. The field of electric effects

        Through different methods Thomson (1987) and Milikan (1910) realized that the electron in a uniform electric field behaves in a similar way to an electric charge with a spherical symmetry. This similarity induces us to consider the uniform electric field as the ideal place to star our analysis.

        Let us imagine a conductive sphere with a long radius and electrically loaded. The electric charge thus imagined produces a practically uniform E Coulomb’s field: it is enough to restrict the domain of the field to small volumes with the longer axis practically non-existent in relationship to the radius of the sphere. The adopted reasoning similar to the one we employ when the gravitational field near the earth is practically uniform.

        In this sphere the electrons are distributed as it is established by Corollary 4: with its main axis perpendicular to the S spherical surface. As the radius of the sphere is quite long, we can represent the electrons as in Figure 6.

        On a generic point P = (x, y, z) in the domain of E field, observing the Superposition Principle it is possible to equate E in this way:

Ei being the contribution of the electron i to the  E field on point P.

Figure 6: Comments in the text.

        One of the possible solutions for the  4.2 equation for Ei of the i electron   is given by Coulomb's equation:

in which K is a proportionality constant related to the definition of an electric field. As we have seen, this solution proved incompatible with many of the experiences made in the 20th century.

        Another solution also compatible with Coulomb’s law in terms of electric charges is:

with qi shown in Figure 6. x will be called electric effects field in order to distinguished from the classic E, which will go on being called electric field. In the present discussion we have: x = S xi = E.

        We shall now demonstrate in a more convincing way that solution 2 (equation 4.4) is actually compatible with Coulomb’s law.