OC:

[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.

I'll make this simple. Thee current is the integral of the
scalar product of the current density and the vector normnal
to the surface bounding the current density. That is a scalar.
Period.

[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.

That is what I wrote. Read it again.

[...]
[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.

So what? Can you determine which is which just by measuring the
magnetic field? No.

[...]
[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?

Are you stoned or just stupid?

[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?

Please use maxwell's equations to describe an electric charge
as a charge density. Use the electron so that I have some nice
experimental numbers to show that any such attempt is wrong.

How is an electric current defined?

How many times do I need to spell it out. I = \integral J.dS

Maxwell's equations relate magnetic fields to currents. Neither of
them is DEFINED in terms of the other.

What's your point?
[...]
[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".

Apparently, you don't read too well. I haven't redefined anything.

When for all physicists electric current is a flow of charge, for you
it is something else.

Try again once you figure out that div cul B = div J = 0 for
magnetostatics.

Could please give us your definition? That would make the discussion
clearer.

I use the same one that appears in ampere's law.

[...]
[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.

What I've written for the current is the only current that appears
in ampere's law.

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).

In which case you don't have a closed loop and magnetostatics does
not apply. In classical E&M,

"OC" wrote in message
om...
[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.

You are your wasting your time with Bilge. Every argument
you have given to Bilge has been given by others also.

Bilge just can't understand it.

Here is what will happen if you continue:
He will either ignore your argument or he will take
a reasonable argument and try and redirect to an
unrelated topic (e.g. in this case magnetism, QM).
Then finally he will skip the arguments and just
continue to insult you. This will be your reward
for trying to explain things to him.

Good luck....

H.Ellis Ensle

"Bilge" wrote in message
...
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.

I think you should be more concerned with your own
understanding of E&M. As long as you can't understand that
current is actually a vector, you do not understand E&M.

H.Ellis Ensle

"Harry" wrote in message
...

"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.

It is well-known? E&M is certainly well-known, but I have never
seen anyone *focus* on this particular point.

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.

OK

H.Ellis Ensle

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

[snip]

I think you should be more concerned with your own
understanding of E&M. As long as you can't understand that
current is actually a vector, you do not understand E&M.

Take a circuit (for example a circular one) with
a constant current running through it.
Got it?
Now show me that constant "current vector" of
yours.

Dirk Vdm

Harold Ensle:


I think you should be more concerned with your own
understanding of E&M. As long as you can't understand that
current is actually a vector, you do not understand E&M.

Answer my questions harold.

[OC]
This sub-thread started because I do not agree with statements saying
that current is a scalar.

In general electric current is not a scalar.

In the particular case of the flux of the current density through a
closed surface, the current is a scalar. But this is not the only
case. And it is not the typical case when dealing with currents.



[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.

[Bilge]
I'll make this simple. Thee current is the integral of the
scalar product of the current density and the vector normnal
to the surface bounding the current density. That is a scalar.
Period.

[OC]
That is not the only case. It is not even the most common.


[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.

[Bilge]
That is what I wrote. Read it again.

[OC]
Can you explain why you introduced Ampere's law (remember that the
problem here is whether the current is a scalar, not what is the
relation between magnetic fields and currents).



[...]
[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]
So what? Can you determine which is which just by measuring the
magnetic field? No.

[OC]
What is the point of introducing magnetic fields?


[...]
[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]
Are you stoned or just stupid?

[OC]
In case you did not notice, the question was about electric current
being a vector.
You introduced magnetostatics and Ampere's law: is this just a
diversion, or is your experience about currents limited to
electromagnets?


[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?

[Bilge]
Please use maxwell's equations to describe an electric charge
as a charge density. Use the electron so that I have some nice
experimental numbers to show that any such attempt is wrong.

[OC]
The integral version of Maxwell's equations do not require necessarily
charge densities and current densities.

Maxwell's equations link magnetic field to currents.
When you say "Maxwell's equations do not explain magnetostatics in
terms of moving charges", you seem to forget that an electric current
IS a flow of charge.
Doesn't this mean that magnetic fields are linked to moving charges?


[OC]
How is an electric current defined?

[Bilge]
How many times do I need to spell it out. I = \integral J.dS

[OC]
Let me rephrase: How is a current density defined?
(And please don't come up with Maxwell's equation or Ampere's law:
that would be incorrect.)


[OC]
Maxwell's equations relate magnetic fields to currents. Neither of
them is DEFINED in terms of the other.

[Bilge]
What's your point?

[OC]
My point is that Maxwell's equations do not define magnetic and
electric fields, nor charge density nor current density.
That means that you cannot use those equations to prove that electric
is a scalar.

[...]
[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".

[Bilge]
Apparently, you don't read too well. I haven't redefined anything.

[OC]
Give your definition of current and current density. Both of them.
Without using Ampere's law or Maxwell's equations (which would be the
wrong way 'round).

[OC]
When for all physicists electric current is a flow of charge, for you
it is something else.

[Bilge]
Try again once you figure out that div cul B = div J = 0 for
magnetostatics.

[OC]
Once mo Maxwell's equation (or Ampere's law) are not a definition
of current or current density.

[OC]
Could please give us your definition? That would make the discussion
clearer.

[Bilge]
I use the same one that appears in ampere's law.

[OC]
Obviously you missed that part where it says that Ampere's law is NOT
a definition of current or current density.

There is no need for Ampere's law (or Maxwell's equations) to DEFINE
current or current density.

(Repetita iuvant?)

[...]
[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.

[OC]
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.

[Bilge]
What I've written for the current is the only current that appears
in ampere's law.

[OC]
Given that we are discussing about the definition of electric current,
Ampere's law is irrelevant.

[OC]
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).

[Bilge]
In which case you don't have a closed loop and magnetostatics does
not apply. In classical E&M,

[OC]
(This last paragraph seems to be incomplete.)

If the problem is the definition of electric current, why are you
talking about magnetostatics? Or about Ampere's law?
None of them has relevance for the topic in the this sub-thread.

OC

"Dirk Van de moortel" wrote
in message ...

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

[snip]

I think you should be more concerned with your own
understanding of E&M. As long as you can't understand that
current is actually a vector, you do not understand E&M.

Take a circuit (for example a circular one) with
a constant current running through it.
Got it?
Now show me that constant "current vector" of
yours.

Who said it was constant? In the case of current in a
wire (of constant cross-section area) the direction of
the current vector at any point is the same as the length
element of the wire. That is why it is typical to make
the length element the vector and leave the current
the scalar. But one can also attach the direction to
the current, leaving the length element as a scalar and
everything comes out the same.

The physical fact is that both are most generally
vectors, but for practical purposes, only one needs to
be considered as such (if the current is confined
to a wire).

Now you show me a constant "velocity vector" for
a fluid constantly flowing in a circular pipe.

H.Ellis Ensle

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


I think you should be more concerned with your own
understanding of E&M. As long as you can't understand that
current is actually a vector, you do not understand E&M.

Answer my questions harold.

I did already many times.

You just didn't get it.

H.Ellis Ensle

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

"Dirk Van de moortel" wrote
in message ...

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

[snip]

I think you should be more concerned with your own
understanding of E&M. As long as you can't understand that
current is actually a vector, you do not understand E&M.

Take a circuit (for example a circular one) with
a constant current running through it.
Got it?
Now show me that constant "current vector" of
yours.

Who said it was constant?

According to every book in the world the "current" of this example
is constant.
The vector that you have in mind is different at every position
of the circuit, and therefore totally useless. If you want to call it a
current, then that is your problem.
But I think that the main problem here is that you are a poor loser.
So, go get your dog out of the kitchen and let it eat that current
http://users.pandora.be/vdmoortel/di...es/WhatIf.html

Dirk Vdm