d F = 0
d★F = 4π★J
much nicer.
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Not with my Firefox/Windows platform...
That is how I learned them the second time. It is certainly prettier.
BLOGWAR!!!!!!!!!!
4pi? If you use God's Own Units (also known as Heaviside-Lorentz) there's no need for the 4pi.
And the first one derives itself so you don't even need to write it down ("The boundary of a boundary is zero!" or something like that shouts Wheeler from beyond his grave.)
notation, notation, notation
that's what it's all about.
If you want to use natural units, as one does, then Green's theorem, in three spatial dimensions, requires a factor of 4pi, which even an astrophysicist will concede is not unity.
Not even approximately.
I personally get slightly queasy absorbing the geometry of space into dimensional units, but hey, de gustibus non est disputandum, eh?
And of course I'm right, and all other notations are inferior and totally suck.
The only reason for the factor of 4pi is to make Coulomb's Law simpler. But if you're doing work where electrostatics doesn't show up much, that is less important. OTOH, if you are studying, say, electromagnetic waves in materials, then having 4pi in Gauss's Law and Ampere's Law means that you get factors of 4pi in your definitions of D and H. It makes things very ugly.
So, ugly equations for waves, dependence of units on spatial dimension, all to make Coulomb's Law simpler.
No thanks.
Maxwell's equation (singular) is even nicer:
âF = J
See the geometric algebra sites of Hestenes and Lasenby for more info.