Re: Conserving Q ? (long)

[Bob Sciamanda <trebor@VELOCITY.NET>]

Note that since there is no real "magnetic charge" current, the
corresponding equation for the curl sources of E has ONLY a "magnetic
displacement" current term:

curl(E) = -dB/dt

There is no real current to be interpreted as both the curl source of E
and the time derivative source of B !

How to consistently give such an interpretation to this equation?

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: Bob Sciamanda <trebor@velocity.net>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Monday, November 23, 1998 10:29 PM
Subject: Re: Conserving Q ? (long)


> David Bowman has shown how Ampere's law can be written as the statement
> that the charge current is both the curl source of B and the time
> derivative source of E;  he also gives strong mathematical motivation
for
> this interpretation, appealing to the electromagnetic field tensor.
>
> I have seen others not only state this view, but adamantly insist that
> this is the only CORRECT interpretation; condemning as heresy the
> interpretation that the charge current and the displacement current are
> both curl sources of B;  David's tone seems more tolerant.
>
> Is this a matter of interpretation; a freely choosable conceptual model
> of the mathematics (a chicken and egg question)?  Or is there a testable
> difference between the two views?
>
> Bob Sciamanda
> Physics, Edinboro Univ of PA (ret)
> trebor@velocity.net
> http://www.velocity.net/~trebor
> -----Original Message-----
> From: David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>
> To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
> Date: Monday, November 23, 1998 12:37 AM
> Subject: Re: Conserving Q ? (long)
>
> > . . .
> > Suppose we return to the case of electric charges (and ignore for now
> > other kinds of locally conserved 'stuff').  We can write Ampere's law
as
> > curl(B) - (1/c^2)*dE/dt = ([mu]_0)*j.  The LHS of this equation (when
> > written in 4-vector/4-tensor notation for Minkowski space) is actually
3
> > (spatial) of the 4 components of the exterior derivative of the dual of
> > the antisymmetric 2nd rank (2-form) electromagnetic field tensor whose
> > space-space components are the components of B and whose space-time
> > components are (up to irrelevant factors of c) the components of E.
The
> > 4th (time) component of this 4-tensor equation is expressed by the
other
> > inhomogeneous Maxwell equation i.e. Gauss' law
> > div(E) = [rho]/[epsilon_0].  Note the current is the source for the
> > composite expression: curl(B) - (1/c^2)*dE/dt which is a part of a
> > single 4-tensor expression in Minkowski space.  We thus see that it is
> > not so much that the displacement current is a source for the magnetic
> > field as that the actual current is a source for a composite
> > combination of *both* the transverse magnetic field *and* part of the
> > time-dependent electric field, i.e. the displacement "current" term
> > when it is not time-steady as well.
> >
> > David Bowman
> > dbowman@georgetowncollege.edu