"Harry" wrote in message
om...
"Harold Ensle" wrote in message
ink.net...

SNIP unnecessary derivation that led to irrelevant criticism

Why is the derivation unnecessary? Some people had clearly
never seen the equations before (and as originally written,
they were not quite correct, having the wrong units).

Why was the criticism irrelevant? The equations were
called invalid because of the current vector issue. Being
invalid would certainly be relevant.

So Tamhane's question is: How can it be that an object
would influence a distant object to move in a direction
perpendicular to the line connecting the two objects UNLESS
it is the REAL magnetic field applying the force?

That is very similar to Feynman's question about the angular momentum
of magnetic field, and his conclusion that "This mystic circulating
flow of energy, which at first seemed so ridiculous, is absolutely
necessary. There is really a momentum flow." Lect.Ph.II Ch.27-11.

Why are you bringing up this unrelated issue?

H.Ellis Ensle

OC:
(Bilge) wrote:
Harold Ensle:
In the thread "Ampere's law proves the reality of the magnetic field"
Tamhane produced a couple of equations:

1: F=(Ia) dot (Ib)/r^2
2: F= (Ia cross r) cross Ib/r^3

These equations are basically correct. Though approximate in
magnitude, they are exact in the direction of the force involved.
Thus, since Tamhane was only interested in the direction of the
force, these equations were sufficient to demonstrate his point.

Bilge, Franz Heyman, and Bill Hobba all claimed that his
equations were wrong because he used a vector current
instead of a scalar current.

Harold, do you _ever_ do anything with any degree of honesty?
I said that current is a scalar. I haven't bothered to check to
see if what he's written resembles anything which is remotely
correct if I assume he doesn't delude himself into doing
something he can't do based upon the way he's written it.

Now, harold. Explain precisely how I = dq/dt or I = \integral J.dS
is a vector. Is charge a vector? Is a scalar product a vector?


Current IS a vector. It does have a direction, doesn't it?

What direction does it point and precisely what is moving? Now consider
two magnets with identical fields. The first is simply a toroidal solenoid
which has a gap in one section and looks like a C-magnet. The other is a
C-magnet made of some ferromagnetic material which is not powered by
anything. Am I going to find any moving charges in the ferromagnet? If
not, then obviously a current density which creates a magnetostatic field,
doesn't depend upon charges flowing at some velocity. Both satisfy the
magnetostatic condition, div J = 0. I leave it to you to find the figure
out what that current ``looks like''.

Even if it is not explicitly stated (the unit vector is omitted in the
definition I=dq/dt, and in the definition with the integral, the
current densisty is more like a vector field).

That contradicts what _is_ explicitly stated. In addition, the current
density is _not_ a vector field. The electromagnetic four-potential, A^u
is a vector field. The current density is the spatial component of the
conserved four-current (density), j^u = (\rho, J).

I am really surprised that there are people that think of a current as
a vector!

Does this mean you will be surprised to read your own argument above

Harold Ensle:

"Harry" wrote in message
. com...
"Harold Ensle" wrote in message
link.net...

SNIP unnecessary derivation that led to irrelevant criticism

Why is the derivation unnecessary? Some people had clearly
never seen the equations before (and as originally written,
they were not quite correct, having the wrong units).

Why was the criticism irrelevant? The equations were
called invalid because of the current vector issue. Being
invalid would certainly be relevant.

You still haven't answered my question about the (non-existent)
electric field from that ``moving line charge as a current''.
In some frame, that line charge is obviously not moving, and
that requires several things which don't agree with the
facts:

(1) Conductors are electrically neutral, yet your description of
a current requires that they have an enormous charge on them,

(2) It implies that a current carrying wire has a radial electric
field, (and a huge one at that), yet that is not what is observed,

(3) It's well-known that a field which is purely magnetic in
one frame, can not be made purely electric in any frame,
yet your definition of a current as a moving charge density
will give a static electric field for any observer moving
at the drift velocity.

Since the typical drift velocity is on the order of 10^-4 m/s, I don't
have to move very fast. According to your definition of a current as a
line charge moving at the drift velocity, let's see how much charge we
should see in the wires around us. A current of 1 ampere corresponds to 1
coulomb/sec. For a drift velocity of 10^-4 m/sec, 1 ampere corresponds to
1 (coulomb/sec)/(10^-4 m/sec), which comes out to be a line charge density
of 10^4 coulombs/meter. What do you suppose the force between two such
line charge densities, each 1 meter in length and separated by 1 meter
turns out to be? (I'll give you a hint: The result has more zeroes on the
left side of the decimal point than your telephone number, including the
area/country code.

"Harold Ensle" wrote in message
nk.net...

"Harry" wrote in message
om...
"Harold Ensle" wrote in message
ink.net...

SNIP unnecessary derivation that led to irrelevant criticism

Why is the derivation unnecessary? Some people had clearly
never seen the equations before (and as originally written,
they were not quite correct, having the wrong units).

Why was the criticism irrelevant? The equations were
called invalid because of the current vector issue. Being
invalid would certainly be relevant.

So Tamhane's question is: How can it be that an object
would influence a distant object to move in a direction
perpendicular to the line connecting the two objects UNLESS
it is the REAL magnetic field applying the force?

That is very similar to Feynman's question about the angular momentum
of magnetic field, and his conclusion that "This mystic circulating
flow of energy, which at first seemed so ridiculous, is absolutely
necessary. There is really a momentum flow." Lect.Ph.II Ch.27-11.

Why are you bringing up this unrelated issue?

H.Ellis Ensle

"Harold Ensle" wrote in message
nk.net...

"Harry" wrote in message
om...
"Harold Ensle" wrote in message
ink.net...

SNIP unnecessary derivation that led to irrelevant criticism

Why is the derivation unnecessary? Some people had clearly
never seen the equations before (and as originally written,
they were not quite correct, having the wrong units).

Well, maybe I misunderstood that your derivation was meant to introduce
Tamhane's question - which relates to a well known fact.

Why was the criticism irrelevant? The equations were
called invalid because of the current vector issue. Being
invalid would certainly be relevant.

There was a lot of criticism that had nothing to do with Tamhane's
rediscovey of the magnetic field.

So Tamhane's question is: How can it be that an object
would influence a distant object to move in a direction
perpendicular to the line connecting the two objects UNLESS
it is the REAL magnetic field applying the force?

That is very similar to Feynman's question about the angular momentum
of magnetic field, and his conclusion that "This mystic circulating
flow of energy, which at first seemed so ridiculous, is absolutely
necessary. There is really a momentum flow." Lect.Ph.II Ch.27-11.

Why are you bringing up this unrelated issue?

That issue is related to your and Tamhane's claim that the magnetic field is
"real". According to Feynman, it is so real that it even really corresponds
to a momentum flow.

Harald

[OC]
Current IS a vector. It does have a direction, doesn't it?

[Bilge]
What direction does it point and precisely what is moving?

[OC]
Doesn't a flow of charge have a direction? Isn't charge flowing from
one point to another?
Aren't charge-carriers moving?

[Bilge]
Now consider
two magnets with identical fields. The first is simply a toroidal solenoid
which has a gap in one section and looks like a C-magnet. The other is a
C-magnet made of some ferromagnetic material which is not powered by
anything. Am I going to find any moving charges in the ferromagnet?

[OC]
Magnetism in matter is a complicated topic.
Electrons have an intrinsic magnetic moment.

[Bilge]
If
not, then obviously a current density which creates a magnetostatic field,
doesn't depend upon charges flowing at some velocity.

[OC]
I said that current is a vector.
You reply by saying there are magnetic fields that are not the result
of moving charges.
That's correct: electrons have an intrinsic magnetic moment that
produces a magnetic field. And this field is not the result of a flow
of charge.
But how does this disprove that a flow of charge is a vector?

[Bilge]
Both satisfy the
magnetostatic condition, div J = 0. I leave it to you to find the figure
out what that current ``looks like''.

[OC]
If you write div J, you are already considering J a vector.
Aren't you contradicting yourself?

(Div J = 0 does not mean that J is a scalar.
If the magnetic field is not produced by a current, then J = 0 and so
div J = 0.)

[OC]
Even if it is not explicitly stated (the unit vector is omitted in the
definition I=dq/dt, and in the definition with the integral, the
current densisty is more like a vector field).

[Bilge]
That contradicts what _is_ explicitly stated. In addition, the current
density is _not_ a vector field. The electromagnetic four-potential, A^u
is a vector field. The current density is the spatial component of the
conserved four-current (density), j^u = (\rho, J).

[OC]
The spatial component of the four-current has THREE components, right?
Isn't that a vector (in 3D space)?
Aren't you contradicting yourself, again?

[OC]
I am really surprised that there are people that think of a current as
a vector!

[Bilge]
Does this mean you will be surprised to read your own argument above

Oh, I mistyped. It should read:
"I am really surprised that there are people that think of a current
as a scalar!"

Anyway, I am surprised that you managed to contradict yourself over
and over again.
Do you read your replies before you post them?

OC

"Bilge" wrote in message
...
Harold Ensle:

"Harry" wrote in message
. com...
"Harold Ensle" wrote in message
link.net...

SNIP unnecessary derivation that led to irrelevant criticism

Why is the derivation unnecessary? Some people had clearly
never seen the equations before (and as originally written,
they were not quite correct, having the wrong units).

Why was the criticism irrelevant? The equations were
called invalid because of the current vector issue. Being
invalid would certainly be relevant.

You still haven't answered my question about the (non-existent)
electric field from that ``moving line charge as a current''.
In some frame, that line charge is obviously not moving, and
that requires several things which don't agree with the
facts:

(1) Conductors are electrically neutral, yet your description of
a current requires that they have an enormous charge on them,

No it doesn't. I=lambda*v where v would be the drift velocity in a
conductor. NO external electric field is required (which is the same
situation with J).

(2) It implies that a current carrying wire has a radial electric
field, (and a huge one at that), yet that is not what is observed,

No it doesn't. (See above).

(3) It's well-known that a field which is purely magnetic in
one frame, can not be made purely electric in any frame,
yet your definition of a current as a moving charge density
will give a static electric field for any observer moving
at the drift velocity.

There is no electric field outside the conductor (classically),
just a magnetic field.

Since the typical drift velocity is on the order of 10^-4 m/s, I don't
have to move very fast. According to your definition of a current as a
line charge moving at the drift velocity, let's see how much charge we
should see in the wires around us. A current of 1 ampere corresponds to 1
coulomb/sec. For a drift velocity of 10^-4 m/sec, 1 ampere corresponds to
1 (coulomb/sec)/(10^-4 m/sec), which comes out to be a line charge density
of 10^4 coulombs/meter. What do you suppose the force between two such
line charge densities, each 1 meter in length and separated by 1 meter
turns out to be? (I'll give you a hint: The result has more zeroes on the
left side of the decimal point than your telephone number, including the
area/country code.

Irrelevant. The only person you are confusing with these digressions
is yourself.

H.Ellis Ensle

Harold Ensle:

"Bilge" wrote in message
e-al.net...
Harold Ensle:

"Harry" wrote in message
. com...
"Harold Ensle" wrote in message
link.net...

SNIP unnecessary derivation that led to irrelevant criticism

Why is the derivation unnecessary? Some people had clearly
never seen the equations before (and as originally written,
they were not quite correct, having the wrong units).

Why was the criticism irrelevant? The equations were
called invalid because of the current vector issue. Being
invalid would certainly be relevant.

You still haven't answered my question about the (non-existent)
electric field from that ``moving line charge as a current''.
In some frame, that line charge is obviously not moving, and
that requires several things which don't agree with the
facts:

(1) Conductors are electrically neutral, yet your description of
a current requires that they have an enormous charge on them,

No it doesn't. I=lambda*v where v would be the drift velocity in a
conductor. NO external electric field is required (which is the same
situation with J).

In that case, your line charge density is zero.

(2) It implies that a current carrying wire has a radial electric
field, (and a huge one at that), yet that is not what is observed,

No it doesn't. (See above).

Yes it does, since you have defined the current to be a line charge
density moving at some velocity. It's still a line charge density.

(3) It's well-known that a field which is purely magnetic in
one frame, can not be made purely electric in any frame,
yet your definition of a current as a moving charge density
will give a static electric field for any observer moving
at the drift velocity.

There is no electric field outside the conductor (classically),
just a magnetic field.

Yes, I know that. That's my point. Your definition of a current
satisfy that and as usual, you don't bother to explain why you
thhink it does or what you think is wrong with my argument.
All you stated was the classical E&M that I used to construct
my argument, which indicates you don't understand classical
E&M.

OC:
[OC]
Current IS a vector. It does have a direction, doesn't it?

[Bilge]
What direction does it point and precisely what is moving?

[OC]
Doesn't a flow of charge have a direction?

Yes. The vector that describes that motion is the velocity of the
charge carriers.

Isn't charge flowing from one point to another?

Recall that in magnetostatics, ampere's law is, curl B = J. There
is no charge anywhere in that equation. There is just a current
density and you can only apply ampere's law to closed loops (infinite
lines are closed at infinity).

Aren't charge-carriers moving?

Since taking the divergence of ampere's law above gives div J = 0
for magnetostatics, the continuity equation requires that d\rho/dt = 0.
Recall that neither ampere nor maxwell had any idea what was going
on inside a wire and that maxwell's equations cannot explain a
current in a wire as moving charges. That requires quantum mechanics
and the first phenomenological theory to make that plausible was
the drude theory of conductors.

[Bilge]
Now consider
two magnets with identical fields. The first is simply a toroidal solenoid
which has a gap in one section and looks like a C-magnet. The other is a
C-magnet made of some ferromagnetic material which is not powered by
anything. Am I going to find any moving charges in the ferromagnet?

[OC]
Magnetism in matter is a complicated topic.

But ampere's law works just fine here. I can draw an amperian loop
for a C-magnet.

Electrons have an intrinsic magnetic moment.

That might be the fundamental explanation, but that fact is not
necessary to use ampere's law on ferromagnets. Ampere's law provides
the explanation of the macroscopic field in terms of a current density
(which one can also draw).

[Bilge]
If not, then obviously a current density which creates a magnetostatic
field, doesn't depend upon charges flowing at some velocity.

[OC]
I said that current is a vector. You reply by saying there are magnetic
fields that are not the result of moving charges.

No, what I said is that current is not a vector and that I don't
need to explain a magnetic field in terms of moving charges to
define a current. Maxwell's equations do not explain magnetostatics
in terms of moving charges. For that matter, maxwell's equations
do not even describe moving charges. The equations describe charge
densities.

That's correct: electrons have an intrinsic magnetic moment that
produces a magnetic field. And this field is not the result of a flow
of charge. But how does this disprove that a flow of charge is a vector?

We aren't talking about the flow of charge. We are talking about
currents.

[Bilge]
Both satisfy the
magnetostatic condition, div J = 0. I leave it to you to find the figure
out what that current ``looks like''.

[OC]
If you write div J, you are already considering J a vector.

J is a vector. It's a current density. The current, I, is the
surface integral of J, I = \integral J . dS, where the `.' means
scalar product.

Aren't you contradicting yourself?

No. My purpose of my argument is to point out the difference
between J, the current density, which is a vector and I which is
a current and is a scalar because it is the integral of J over
a surface.

[OC]
Even if it is not explicitly stated (the unit vector is omitted in the
definition I=dq/dt, and in the definition with the integral, the
current densisty is more like a vector field).

[Bilge]
That contradicts what _is_ explicitly stated. In addition, the current
density is _not_ a vector field. The electromagnetic four-potential, A^u
is a vector field. The current density is the spatial component of the
conserved four-current (density), j^u = (\rho, J).

[OC]
The spatial component of the four-current has THREE components, right?
Isn't that a vector (in 3D space)?
Aren't you contradicting yourself, again?

Why? I said that J wasn't a vector field, at least not in the sense
that field is used in physics, which is consistent with the distinction
you attempted to make between I being a vector and J being a vector
field. Define what you mean by vector and vector field, and I won't
have to guess.

[...]

Anyway, I am surprised that you managed to contradict yourself over
and over again.

You shouldn't be surprised. You created the contradictions by making
inferences which either weren't implied in what I wrote or contradict
what I wrote.

Do you read your replies before you post them?

Do you read my replies before you respond to them?

[OC]
Current IS a vector. It does have a direction, doesn't it?

[Bilge]
What direction does it point and precisely what is moving?

[OC]
Doesn't a flow of charge have a direction?

[Bilge]
Yes. The vector that describes that motion is the velocity of the
charge carriers.

[OC]
Isn't charge flowing from one point to another?

[Bilge]
Recall that in magnetostatics, ampere's law is, curl B = J. There
is no charge anywhere in that equation. There is just a current
density and you can only apply ampere's law to closed loops (infinite
lines are closed at infinity).

[OC]
There is a non-zero current density. That means that there are
charge-carriers moving around, which means that there is a charge
flow.


[OC]
Aren't charge-carriers moving?

[Bilge]
Since taking the divergence of ampere's law above gives div J = 0
for magnetostatics, the continuity equation requires that d\rho/dt = 0.

[OC]
The continuity equation means that the d/dt of the total charge withIN
a volume equals the total flux of the current through the surface that
encloses that volume.
If there is a steady non-zero current, the net charge of a (arbitrary)
volume is constant in time.

[Bilge]
Recall that neither ampere nor maxwell had any idea what was going
on inside a wire and that maxwell's equations cannot explain a
current in a wire as moving charges. That requires quantum mechanics
and the first phenomenological theory to make that plausible was
the drude theory of conductors.

[Bilge]
Now consider
two magnets with identical fields. The first is simply a toroidal solenoid
which has a gap in one section and looks like a C-magnet. The other is a
C-magnet made of some ferromagnetic material which is not powered by
anything. Am I going to find any moving charges in the ferromagnet?

[OC]
Magnetism in matter is a complicated topic.

[Bilge]
But ampere's law works just fine here. I can draw an amperian loop
for a C-magnet.

[OC]
Electrons have an intrinsic magnetic moment.

[Bilge]
That might be the fundamental explanation, but that fact is not
necessary to use ampere's law on ferromagnets. Ampere's law provides
the explanation of the macroscopic field in terms of a current density
(which one can also draw).

[OC]
But it does not exclude magnetic fields not produced by currents.


[Bilge]
If not, then obviously a current density which creates a magnetostatic
field, doesn't depend upon charges flowing at some velocity.

[OC]
I said that current is a vector. You reply by saying there are magnetic
fields that are not the result of moving charges.

[Bilge]
No, what I said is that current is not a vector and that I don't
need to explain a magnetic field in terms of moving charges to
define a current.

[OC]
Why do you need the magnetic field in the first place?

[Bilge]
Maxwell's equations do not explain magnetostatics
in terms of moving charges. For that matter, maxwell's equations
do not even describe moving charges. The equations describe charge
densities.

[OC]
And charge densities are not related to charges?
How is an electric current defined?
Maxwell's equations relate magnetic fields to currents. Neither of
them is DEFINED in terms of the other.
Maxwell's equations do not define the terms they use: they relate
them.


[OC]
That's correct: electrons have an intrinsic magnetic moment that
produces a magnetic field. And this field is not the result of a flow
of charge. But how does this disprove that a flow of charge is a vector?

[Bilge]
We aren't talking about the flow of charge. We are talking about
currents.

[OC]
So, apparently you must have redefined the term "electric current".
When for all physicists electric current is a flow of charge, for you
it is something else.
Could please give us your definition? That would make the discussion
clearer.


[Bilge]
Both satisfy the
magnetostatic condition, div J = 0. I leave it to you to find the figure
out what that current ``looks like''.

[OC]
If you write div J, you are already considering J a vector.

[Bilge]
J is a vector. It's a current density. The current, I, is the
surface integral of J, I = \integral J . dS, where the `.' means
scalar product.

[OC]
That is the flux of current through a closed surface.

Apparently our disagreement arises from the fact that you have this
integral in mind (where I, as a flux, is a scalar), while I have other
cases in mind.

For example, if you consider a wire, you can define the total current
as the flux of the current density through the cross-section (which is
not a closed surface).


[OC]
Aren't you contradicting yourself?

[Bilge]
No. My purpose of my argument is to point out the difference
between J, the current density, which is a vector and I which is
a current and is a scalar because it is the integral of J over
a surface.

[OC]
As I said above, the I you have in mind is the flux through a closed
surface.


[OC]
Even if it is not explicitly stated (the unit vector is omitted in the
definition I=dq/dt, and in the definition with the integral, the
current densisty is more like a vector field).

[Bilge]
That contradicts what _is_ explicitly stated. In addition, the current
density is _not_ a vector field. The electromagnetic four-potential, A^u
is a vector field. The current density is the spatial component of the
conserved four-current (density), j^u = (\rho, J).

[OC]
The spatial component of the four-current has THREE components, right?
Isn't that a vector (in 3D space)?
Aren't you contradicting yourself, again?

[Bilge]
Why? I said that J wasn't a vector field, at least not in the sense
that field is used in physics, which is consistent with the distinction
you attempted to make between I being a vector and J being a vector
field. Define what you mean by vector and vector field, and I won't
have to guess.

[OC]
Considering the current density as a vector field is the same as for
the electric or magnetic field.

What is the problem in considering the current as a vector?

[OC]
Anyway, I am surprised that you managed to contradict yourself over
and over again.

[Bilge]
You shouldn't be surprised. You created the contradictions by making
inferences which either weren't implied in what I wrote or contradict
what I wrote.

[OC]
Yes, apparently I did not fully understand what you wrote.
Now things are much clearer.

OC