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. But as demonstrated by Griffiths
("Introduction to Electrodynamics" 202-204) it is possible to
use a vector current and obtain the correct answers.

In the proccess of arguing about the benifits of vector current
on that thread, I derived Tamhane's equations, but unfortunately,
I did it terribly!

I would like to redo the derivation here in the hopes that by
people understanding Tamhane's equations, they will better
understand his very clever argument.

Imagine a length element dla of a current Ia in a magnetic field B.
The force for a current in a magnetic field can be derived from
the Lorentz force law which gives:

F=integral(Ia cross B)dla (from Griffiths eq. 5.15)________1

Now imagine that the magnetic field is being created by a current Ib
over a length lb. The equation for the magnetic field B is then:

B=mu/4pi integral((Ib cross r)/r^3)dlb (from Griffiths eq. 5.28)_2

Now substituting this into equation (1) yields:

F=integral(Ia cross (mu/4pi integral((Ib cross r)/r^3)dlb)dla___3

Now imagine that we will use very short segments of equal length
so that la=lb=L=very short. We will also have enough distance
between them so that over the integral to a good approximation,
the distance r does not vary. For these short segments and
sufficient separation, everything comes out of the integrals thus:

F=muL^2/4pi Ia cross (Ib cross r)/r^3___________________4

The interesting thing about this equation is that it is the
magnetic analogy to coulomb's law as it gives a direct force relation
between two short segments of current. It is not a perfect analogy
since the current can't be a point or else L=0 and thus F=0. But
it is sufficient for the purposes at hand.

To understand the direction of the force, it is useful to apply an
identity which yields:

F=muL^2/4pi( Ib(Ia dot r)/r^3 - (Ia dot Ib)/r^2 )___________5

The direction of the first term is the same as Ib and the second
term has the direction of the separation r. (r is the scalar
magnitude in the denominator.)

Now if the currents are in parallel planes, then (Ia dot r)=0 and the
only force is between the two segments. But if one current is toward
the other while one is orthagonal, then (Ia dot Ib)=0 and the force
is in the direction of Ib.

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?

This is also a problem for SR since the usual SR explanation
explains magnetism as an excess electric field as seen from
a particular frame of reference...BUT since the electric field
(in the quasi-static limit) always points in the direction of
the line connecting the two objects, SR apparently does not
fully explain amperes law.

Thanks to Tamhane for bringing up this very interesting point.

H.Ellis Ensle

"Harold Ensle" wrote in message
nk.net...
| 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. But as demonstrated by Griffiths
| ("Introduction to Electrodynamics" 202-204) it is possible to
| use a vector current and obtain the correct answers.
|
| In the proccess of arguing about the benifits of vector current
| on that thread, I derived Tamhane's equations, but unfortunately,
| I did it terribly!
|
| I would like to redo the derivation here in the hopes that by
| people understanding Tamhane's equations, they will better
| understand his very clever argument.
|
| Imagine a length element dla of a current Ia in a magnetic field B.
| The force for a current in a magnetic field can be derived from
| the Lorentz force law which gives:
|
| F=integral(Ia cross B)dla (from Griffiths eq. 5.15)________1
|
| Now imagine that the magnetic field is being created by a current Ib
| over a length lb. The equation for the magnetic field B is then:
|
| B=mu/4pi integral((Ib cross r)/r^3)dlb (from Griffiths eq. 5.28)_2
|
| Now substituting this into equation (1) yields:
|
| F=integral(Ia cross (mu/4pi integral((Ib cross r)/r^3)dlb)dla___3
|
| Now imagine that we will use very short segments of equal length
| so that la=lb=L=very short. We will also have enough distance
| between them so that over the integral to a good approximation,
| the distance r does not vary. For these short segments and
| sufficient separation, everything comes out of the integrals thus:
|
| F=muL^2/4pi Ia cross (Ib cross r)/r^3___________________4
|
| The interesting thing about this equation is that it is the
| magnetic analogy to coulomb's law as it gives a direct force relation
| between two short segments of current. It is not a perfect analogy
| since the current can't be a point or else L=0 and thus F=0. But
| it is sufficient for the purposes at hand.
|
| To understand the direction of the force, it is useful to apply an
| identity which yields:
|
| F=muL^2/4pi( Ib(Ia dot r)/r^3 - (Ia dot Ib)/r^2 )___________5
|
| The direction of the first term is the same as Ib and the second
| term has the direction of the separation r. (r is the scalar
| magnitude in the denominator.)
|
| Now if the currents are in parallel planes, then (Ia dot r)=0 and the
| only force is between the two segments. But if one current is toward
| the other while one is orthagonal, then (Ia dot Ib)=0 and the force
| is in the direction of Ib.
|
| 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?
|
| This is also a problem for SR since the usual SR explanation
| explains magnetism as an excess electric field as seen from
| a particular frame of reference...BUT since the electric field
| (in the quasi-static limit) always points in the direction of
| the line connecting the two objects, SR apparently does not
| fully explain amperes law.
|
| Thanks to Tamhane for bringing up this very interesting point.
|
| H.Ellis Ensle

Bilge, Franz Heymann, Bill Hobba, Robert Kolker, Dirk van der moortel, David
Evens, David Smith and Varney are all incompetent fools that think they are
knowledgeable. Not one of them can carry on a reasoned debate.
Androcles

"Androcles" wrote in message ...


Bilge, Franz Heymann, Bill Hobba, Robert Kolker, Dirk van der moortel, David
Evens, David Smith and Varney are all incompetent fools that think they are
knowledgeable. Not one of them can carry on a reasoned debate.
Androcles

Example of a reasoned debate by John Androcles Farter:
http://users.pandora.be/vdmoortel/di...ndrorgasm.html

Dirk Vdm

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?

"Dirk Van de moortel" wrote
in message news |
| "Androcles" wrote in message
...
|
|
| Bilge, Franz Heymann, Bill Hobba, Robert Kolker, Dirk van der moortel,
David
| Evens, David Smith and Varney are all incompetent fools that think they
are
| knowledgeable. Not one of them can carry on a reasoned debate.
| Androcles
|
| Example of a reasoned debate by John Androcles Farter:
| http://users.pandora.be/vdmoortel/di...ndrorgasm.html
|
| Dirk Vdm
Example of a reasoned debate by Dinky the Deranged:
"Dirk Van de moortel" wrote
in message ...

"Androcles" wrote in message
...

"Dirk Van de moortel"
wrote
in message ...
some garbage to propagate his smear campaign.

So you really don't want to discuss relativity, then, Dinky?

Discuss relativity?
With a load of crap like you?
http://users.pandora.be/vdmoortel/di.../LoadCrap.html
HAHAHAHAHAHAHAHAHAHAHAHAHA!
You are about as funny as Wilson Rabbidge!

Dirk Vdm
Of course, Dinky the Deranged isn't funny at all, he is just there to be
scoffed at.
http://www.androc1es.pwp.blueyonder....rtalFumble.htm
http://www.androc1es.pwp.blueyonder.co.uk/Andersen's%20Nemesis.htm

http://www.androc1es.pwp.blueyonder....ivist_ande.htm
http://www.androc1es.pwp.blueyonder....Transforms.htm
http://www.androc1es.pwp.blueyonder....nd%20Faith.htm
http://www.androc1es.pwp.blueyonder....al_rev_2.3.htm
http://www.androc1es.pwp.blueyonder....dio%20Wave.htm
http://www.androc1es.pwp.blueyonder....ekerinTime.htm
http://www.androc1es.pwp.blueyonder....ctual_data.htm
http://www.androc1es.pwp.blueyonder....irus_alert.htm
http://www.androc1es.pwp.blueyonder....Copernicus.htm
http://www.androc1es.pwp.blueyonder....CplusVstar.htm
http://www.androc1es.pwp.blueyonder.co.uk/cheating.htm
http://www.androc1es.pwp.blueyonder.co.uk/Theorem.htm
http://www.androc1es.pwp.blueyonder.co.uk/Pulsar.htm
http://www.androc1es.pwp.blueyonder....with_stars.htm
http://www.androc1es.pwp.blueyonder.co.uk/gardner.htm
http://www.androc1es.pwp.blueyonder.co.uk/EDoppler.htm
http://www.androc1es.pwp.blueyonder...._revisited.htm

http://groups.google.com/groups?hl=e...r.co.uk&rnum=1
Androcles

"Bilge" wrote in message
...
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?

Absolutely Bilge. In discussions with me he claimed (speaking of 1.)
'Tamhane's equation is the force between two current elements of any
orientation'. Which of course does not solve the problem they are wrong for
two parallel current carrying wires. To resolve this he wants to draw a
distinction between currents and currents in infinitely long parallel wires.
He just makes it up as he goes along. Simple as that.

Thanks
Bill

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?

"Bilge" wrote in message
...
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?

Always...If you think I have lied.....be specific.

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.

You wrote in response to Tamhane:
"Currents are _NOT_ vectors. Currents are _scalars_."

It immediately follows that you would think that his equations
are wrong since he used a vector current.
Though I thought that you had explicitly stated it (as did the
others), but apparently you did not.

So I retract my above statement that you "stated" it, but
I think that your response _clearly_ indicated it.


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

As I explained 100 times already...neither of these are vectors.
Did you read any of my posts or not? Here I will repeat a
response I gave to Hobba which I think clarifies it. He was
defining current as I=dq/dt...............

What you [Hobba] fail to realize is that this definition has all sorts of
hidden
assumptions and so it is not the most general definition of current.
Since charge is conserved dQ/dt _never happens_ UNLESS you
consider a finite region of space and MOVE charges in or out of
the region. To move charge you have to move electrons(#)....to move
electrons you have to give them a velocity.....and velocity is a vector.
So while one can use the above definition (I=dQ/dt) to solve various
problems, it is Griffith's definition that is the most general.
[Griffiths definition being I=lambda*v]

# It could be any charged particle, I just picked electrons because
they are the usual candidates.

H.Ellis Ensle

Harold Ensle:

"Bilge" wrote in message
ue-al.net...
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?

Always...If you think I have lied.....be specific.

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.

You wrote in response to Tamhane:
"Currents are _NOT_ vectors. Currents are _scalars_."

That is correct. I wrote that currents are scalars and currents
_are_ scalars. That is not what you said above. Moron.

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

SNIP unnecessary derivation that led to irrelevant criticism

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.

Harald

(Bilge) wrote in message ...
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?
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).

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

OC