﻿ The Dependence of Force on the Product of Charges Implies the Discretization and Spatial Distribution of the Charges
San José State University

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The Dependence of Force
on the Product of Charges
Implies the Discretization and
Spatial Distribution of the Charges

The force between two bodies of elecrical charges q and Q is given by the Coloumbic formula

#### F = kqQ/s²

where k is a constant and s is the separaration distance between them. The dependence on the product qQ raises the question of how Nature can generate a product of two real numbers. How would Nature generate the product of two irrational numbers such as √2 and √3? The dependence of force on inverse distance squared is handled by the force being propagated by particles that are spread over an area of 4πs² and so their intensity is diminished by this factor.

It is conjectured here that the product of charges is generated by a charge being composed of discrete spatially separated units. Let n and N be the numbers of these discrete units for the charges of q and Q, respectively. Nature establishes the force between two discrete units at a separation distance s. One unit of the charge q then interacts with the N units of the charge Q. There are n units for the charge q so the number of interactions is automatically nN. The force between the charges is then proportional to nN and hence also to qQ.

The gravitational force between masses of magnitudes m and M also depends upon the product mM.

#### F = GmM/s²

All of the force formulas show this dependence so all of the generic charges are composed of discrete units spatially separated.

The product dependence has the special property that if the charges are decomposed such that ∪qi=q and ∪Qj=Q with no overlaps and the differences in separation distances being insignificant then

#### F = kqQ/s² = Σi Σj kqiQj/s²

Thus the dependence has to be on the product of the charges.