Re: Measuring the vector potential

On 19 Oct, 00:27, maxwell <s...@xxxxxxx> wrote:
On Oct 13, 9:21 am, blackhead <larryhar...@xxxxxxxxxxxx> wrote:





On 13 Oct, 16:39, maxwell <s...@xxxxxxx> wrote:

On Oct 12, 4:23 pm, blackhead <larryhar...@xxxxxxxxxxxx> wrote:

On 10 Oct, 20:01, maxwell <s...@xxxxxxx> wrote:

On Oct 9, 7:04 pm, blackhead <larryhar...@xxxxxxxxxxxx> wrote:

On 9 Oct, 21:21, "Bill Miller" <billmillerkt...@xxxxxxxxxxxxxxxx>
wrote:

"blackhead" <larryhar...@xxxxxxxxxxxx> wrote in message

news:1191608697.381957.118940@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

On Sep 27, 8:38 pm, "Bill Miller" <billmillerkt...@xxxxxxxxxxxxxxxx>
wrote:
Hell "Mr. E"... Please see below...

"Mr. Entropy" <egi...@xxxxxxxxx> wrote in message

news:1190920163.750141.255400@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Hi, Bill

On Sep 26, 5:40 pm, "Bill Miller" <billmillerkt...@xxxxxxxxxxxxxxxx>
wrote:
Its intensity is proportional to the rate of change of current flow
and
inversely proportional to r (distance) and to cSQR. It is equal to the
negative time derivative of A, the magnetic vector potential. or,
Ek= -dA/dt.

Yes, that's exactly what I was thinking. But that would mean that
Gauss' law, which fails to distinguish E from Ek, is incorrect in the
presence of varying currents. If that's true, wouldn't it be common
knowledge by now?

Up 'til now it has been masked by at least three issues. The first is the
idea that an E field can *cause* an H field. The second is that an H
field
can *cause* an E field. The third is Lentz's law.

The first has been proven empirically false since no one has ever been
able
to measure the Magnetic field "caused" by Displacement Current.

The second has been masked by the assumption that induction is a
magnetic
effect when it is an interaction between the movement of charges as
manifested by Ek.

The third has been *ignored*. This is Lentz's law, an interactive
property
that has remained unexplained/unexplainable since it was determined
empirically way back when. The equations that define Ek show how and why
Lentz's law "works" the way it does.

I haven't read Jefimenko's work, but I've come to the conclusion that
E of a charge moving in a charge distribution acts upon that
distribution which in turn acts back on the charge so creating an E
with components parallel and normal to the charge's motion. That which
is normal to the charge's motion is interpteted as the B component
because it does no work, that which is parallel is the E component
because it does work. Is this similar to what Jefimenko has in mind?

Nope...

Jefimenko's proposition is that Maxwell's equations are descriptive; not
causative. He maintains Maxwell's independent definitions of E and H and
assumes their properties are pretty much the same as has always been
postulated.

He shows that their causes are charges and the motion of charges. Since both
E and H have the same root causes, this is why a time varying E is always
associated with a time varying H, and vice-versa.

Unfortunately, Jefimenko's work is "equation rich" and no one (that I know
of) has published any simplified versions with diagrams etc.

The only other place to which I can point you would be Wikepedia. Search for
"Jefimenko's Equations." This will at least show you the structure and
layout of the equations.

I hope this helps!

Bill

His equations don't look as useful as the Lienard-Wiechert potentials
or E and B for a moving charge.

I hope this helps. There's lots more, and that's why I was "ragging" on
Benj. Much of the "stuff" that he (and I) are interested in is covered by
Jefimenko's work.

Thanks much for the reference,

You're welcome!

Bill

Mr. E- Hide quoted text -

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Well put, Bill. It's hard to get people to think about the physics
when they are only examined on the math.
The L-W potentials are derived using a 'small' volume filled with
electric fluid (popularly known as 'charge density'). The 'back' of
this volume reacts to the 'target' (field) point at a slightly
different time than the 'front', hence the retarded factor.

Who's point are you answering?

The back of the charge reacting to the observation point is just plain
stupid.

There is a retarded factor because the contributions to the potential
at an observation point for charges moving are different compared to
if the charges were static but at the same positions.

Take two charges q1 @r1, q2 @r2 with r1 > r2, dr = r1 - r2, parallel
and both travelling at velocity v away from and along r1, r2. The
observation point is at r = 0. The potential of q1 that arrives at q2
is from a retarded time t' = dr/(v + c). This is when q1 was at r2 +
dr - vt' = r2 + dr - v dr/(v + c) = r2 + dr/(1 + B) where B = v/c. So
the potential at the observation point can be replaced by an
equivalent static q1 and q2 seperated by dr/(1 + B), equivalent to
increasing the charge density by (1 + B) at r.

Finally
the limit is taken of shrinking the volume to zero for a 'point'
charge. Good luck trying to derive this result, ab initio, from the
defininition of a real point-particle, with no finite size, like the
electron.- Hide quoted text -

Yes, the factor is still there as the size tends towards zero for an
electron.

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Please learn to read. I wrote "ab initio" not "tends towards zero".
This was my point that Maxwellian EM is based on extended charge
definitions not point charges; ah well, they just don't teach Latin
anymore.- Hide quoted text -

- Show quoted text -

My derivation used 2 point charges to show that the (1 + B) factor is
independent of their seperation, dr. I didn't use extended charges.

Still awaiting your derivation. All derivations of L-W I have seen
use a finite separation to generate a factor from the difference in
transmission times,
Is this what you have done?- Hide quoted text -

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Yes, I am doing this. My crude derivation is further up the thread,
but I'll repeat it here:-
Take two charges q1 @r1, q2 @r2 with r1 > r2, dr = r1 - r2, parallel
and both travelling at velocity v away from and along r1, r2. The
observation point is at r = 0. The potential of q1 that arrives at q2
is from a retarded time t' = dr/(v + c). This is when q1 was at r2 +
dr - vt' = r2 + dr - v dr/(v + c) = r2 + dr/(1 + B) where B = v/c. So
the potential at the observation point can be replaced by an
equivalent static q1 and q2 seperated by dr/(1 + B), equivalent to
increasing the charge density by (1 + B) at r.

The total potential is then q2/r2 + q1/(r2 + dr(1 + B)) which for
small dr and q1 = q2 can be written:

q/r2 + q/r2 (1 - dr(1 + B)/r2)

= 2q/r2 - q dr(1 + B)/r2^2 )

I'm not sure how to proceed further, since I was hoping to end up with
an expression 2q/(1 + B) r2. Maybe I've made an error some where...

.

Relevant Pages

  • Re: 1 FERTZ
    ... charge density and current density in a vacuum (after all, ... the derivation for other media would be similar. ... Phi and A are not uniquely defined; one can make a so-called "gauge ... So we see that the potentials have the *same* time dependence as the ...
    (sci.physics.particle)
  • Re: 1 FERTZ
    ... charge density and current density in a vacuum (after all, ... the derivation for other media would be similar. ... Phi and A are not uniquely defined; one can make a so-called "gauge ... So we see that the potentials have the *same* time dependence as the ...
    (sci.physics)
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  • Re: Measuring the vector potential
    ... E of a charge moving in a charge distribution acts upon that ... The L-W potentials are derived using a 'small' volume filled with ... Still awaiting your derivation. ...
    (sci.physics.electromag)
  • Re: 1 FERTZ
    ... > The calculation I referred to above can be found in any textbook. ... > Keep in mind that B and E are vector fields, ... > charge density and current density in a vacuum (after all, ... the derivation for other media would be similar. ...
    (sci.physics.particle)