Here again I am going to start teaching electricity. What will
I do with epsilon_zero this time? I always curse those who
decided to place epsilon_zero into the Coulomb Law. Please
let me know if you see anything heretical below.
After introducing Coulomb's law in terms of F=k*Q1*Q2/r^2,
where k is simply a proportionality constant, I will say this.
Let us invent our own unit of Q and call it S (after Satan). The
immediate consequence of this is that the unit of k must be
N*m^2/S^2. What is the numeric value of k? It depends on
how large is one S. If S is large then k is small, and vice versa.
Suppose we arbitrarily declare that a point charge Q is 1S when
the force it exerts on another point charge of 1S, situated 2 meter
away, is 7 N. Why seven? Because each week has exactly seven
days. And why two? Because it is the smallest even number.
What must the numerical value of k be to reflect this arbitrary
choice of the unit of charge? The answer, according to Coulomb's
law, is k=28 N*m^2/S^2. By a similar kind of reasoning the SI
designers adopted another unit of Q named Coulomb, C. A point
charge of one microcoulomb acts on another point charge of
that magnitude with a force of 1 N when the distance between
charges is 9.4815 cm. Why 9.4815? Why not? Any choice is as
good as any other choice, at least in principle, as long as we all
agree to respect it.
Please verify that the above definition of Coulomb implies that
k=8.99*10^9 N*m^2/C^2. It turns out that 4*Pi can be eliminated
from some derived formulas if k is written 1/(4*Pi*epsilon_zero),
where epsilon_zero is 8.8542*10^-12 C^2/(N*m^2). The name
given to epsilon_zero, "permittivity of free space", can not be
appreciated in this introductory physics course.
Ludwik Kowalski