Write out Maxwell's equations in this system of units.
(Hint: We must have
We have set
so we must set
to ensure c=1. Then COULOMB'S LAW reads
which, integrated over a sphere
centred on the charge, gives
, so GAUSS' LAW has
a where the used to be, just as expected.
By the same token we expect to replace by
in the AMPÈRE/MAXWELL LAW; so Maxwell's equations
where both sides of each equation are measured in units of s-3.
These are of course the "microscopic" equations;
if we want to use the "macroscopic average" fields
we must include a dimensionless permittivity
(where is the dielectric constant)
and dimensionless permeability
(where is the magnetic susceptibility).
That was pretty simple. But before you get too enthusiastic,
you might want to make a quantitative calculation of
your own weight or the electron's charge
in these units. For the former I get something like
1058 s-2. (I wouldn't want to have to paint the dials
on bathroom scales if the world embraced these particular
"natural units"!)3One can also set Newton's universal gravitational constant G=1
to define PLANCK UNITS, but I don't understand how that works.
We already have everything covered, as far as I can see.