Re: Why do permitivity and permiability appear in EM expressions?
- From: Tom Potter <tdp1001@xxxxxxxxx>
- Date: 30 Apr 2007 05:17:22 -0700
On Apr 29, 11:18 pm, "Ireckon" <jpola...@xxxxxxxxxx> wrote:
"Michael Moroney" <moro...@xxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:f12i4r$s0j$1@xxxxxxxxxxxxxxxx
hetware <massl...@xxxxxxxxxxxx> writes:
Michael Moroney wrote:
where epsilon_o and mu_o are specific to the vacuum. Clearly mu_o was
chosen for someone's convenience, but why?
The ampere is defined not as coulombs or so many electrons per second,
but
as the current in two infinitely long parallel wires 1 meter apart that
produces a force of 2*10^-7 newtons per meter between them. The coulomb
is defined in terms of the ampere, not the other way around. The value
of mu_0 falls out of that constant.
That sounds like an informed description. I have to wonder what
relationship the epsilon_o and mu_o have to their un-subscripted
counterparts which appear in the equations dealing with EM permeating bulk
materials. That is to say, which is the chicken, and which is the egg,
wrt, defined values and/or units?
E_0 and mu_0 fall out of the choice of units and such things as the
observed force between two charges and Maxwell's equations. I'd think
E and mu of a bulk substance are based on E_0 and mu_0 and the
electromagnetic properties of the substance.
What would the consequences of
choosing a different value for mu_o be? That is other than the obvious
need to adjust epsion_o so that c comes out right.
Assuming we keep the same definition of meter and newton, it means we
chose a different constant instead of 2*10^-7 newtons to define the
ampere. This would mean the definition of an ampere would have a
different
value than the one we know, and therefore the definition of a coulomb
would differ, and therefore the force between two "1 coulomb" charges
will
differ (since we have a different definition of a coulomb), and from
this,
we'll see a different value of e_0.
Something seems amiss with this. The value of a coulomb seems a
reasonable
candidate for absorbing any adjustments.
Well, it isn't. The coulomb is defined in terms of the ampere and the
second, 1 coulomb is 1 ampere-second. Change the definition of the ampere
(or the second) and you change the definition of the coulomb.
The ampere was somewhat arbitrarily defined in terms of a force in a
certain configuration of current (two infinitely long wires at a given
distance).
If it were me, I'd define the coulomb as fundamental or in terms of the
forces between charges at a fixed distance, and the ampere as 1 coulomb
per second, since charge is a fundamental property of the electron and
magnetism is from charges in motion (current), but they didn't ask me.
Since the electron isn't going to change its charge, the magic number
e=1.602*10-19 C will be different because the coulomb is different.
And is there a downside to that?
No, just a different number to remember.
Things get rough when you drop eps0 as they do in cgs units.
In real mks physics, the electric field is given by
E = q/4pi eps0 r^2 volts/meter
where q is coulombs and eps0 coul/volt-meter (same as eps0 = farad/meter.
In cgs they think they are "throwing away" 4pi eps0
to get E = q/r^2 but you can't do that to real physics. Instead eps0 is
absorbed into the charge unit q
that now has to change from q coulombs to q/eps0 = e.s.u. = q' volt-meters.
Then E = q/r^2 will deliver volts/meter. But there no longer is a coulomb in
cgs units. And you will not see anyone trying to affix any
units, just "e.s.u" which as I said are Volt-Meters.
Now when you bring up a second charge to get force between them, it also has
been corrupted
into swallowing 1/4pieps0, so you have to use "Coulombs Constant" = 4pieps0
to convert the 2d
one back into coulombs.
You're taking it all too casually and relying in the last ditch on coulombs,
and it is hard to notice
when they are taken away. It is seldom discussed.
John Polasek- Hide quoted text -
- Show quoted text -
Good points!
--
Tom Potter
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