San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

The exponent of charge variables
in physical law must be unity
in order for them to apply
to distributed charges

Let Z be a physical charge such as gravitational mass or electric charge for some physical body, that determines some variable E in the form

E = αZβ

where α and β are parameters.

Suppose now that the body is divided up into m equal proportions. The amount per portion is then α(Z/m)β and the total is

Em = αZβ/mβ-1

and therefore

limitm→∞ Em = 0 if β>1
=αZ if β=1
=sgn(α)*∞ if β<1

Thus only the case of β equal to 1 is meaningful physically.

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