A well-bred person never conceals 4 pi or Coulomb's constant. To do so is on par with cheating at cards.
Coulomb's law is
F = kCQQ'/r2
where the constant kC is called Coulomb's constant. It says that the force between a pair of point-charges is proportional to the product of the two charges divided by the square of the separation—analogous to Newton's law of gravitation.
In Planck units the elementary charge e serves as the unit of charge and the Coulomb constant is
kC = alpha Planck force (Planck length)2/e2 = alpha h-bar c/e2.
alpha is commonly written 1/137. It's called the fine structure constant and is the value of the Coulomb constant in Planck units.
Coulomb's inverse-square law was discovered by Henry Cavendish prior to Coulomb, but the result went unpublished until after his death. Cavendish had verified the inverse square character of the force to within 2 percent. Coulomb's work was published in several issues of the Mémoirs de l'Académie Royale between 1775 and 1779. Had Cavendish published his work we would presumably call this constant the "Cavendish constant."
Coulomb's constant occurs in Gauss's law, where the electric field integrated over a closed surface (the normal component, to give the flux out of the region bounded by the surface) is related to the charge Q enclosed inside the surface. In fact the flux integral, according to Gauss's law, turns out to be
4 pi kCQ
The 4 pi and the kC intuitively belong in Gauss's law. Their physical meaning stands out if one thinks of the simplest case: a sphere enclosing a point charge. Then kC (the operative form of alpha) provides for the genesis of the field and the 4 pi is associated with the area of the closed surface over which the field is integrated. Moral degenerates replace 4 pi kC by the reciprocal of its reciprocal or (if you prefer) the inverse of its inverse, thus taking a doubly inverted approach. They define a phoney constant epsilono as (4 pi kC)-1 and then rewrite the original expression as ( (4 pi kC)-1)-1Q or, as one sees in SI textbooks, (epsilono)-1Q. Someday, when the world is a better place, an end will be put to SI sillyness.
Copyright © 2002 by Leonard Cottrell. All rights reserved.