| Topic: |
Science > Physics |
| User: |
"V.K.Tamhane" |
| Date: |
17 May 2004 06:37:41 AM |
| Object: |
Ampere's law proves reality of magnetic field |
Let us first ponder over force acting at a distance. Whenever there
exists such a force between two bodies, the force vector always lies
between them. The bodies, depending on their nature, either attract or
repel in the direction of the line joining them. Force between two
current elements is a bit complex, because sources are vectors and so,
justifiably, we can say that, in this case, the force depends not only
on magnitude but also on the orientation of the sources as well. Hence
for the magnetic force, we have following Biot-Savart law (neglect
constants),
F=(Ia) dot (Ib)/r^2 ………………………1.
Where Ia and Ib are two parallel current elements in the y
direction, having a distance vector r in the x direction.
This dot product should have been the final word. It is not!
Correct equation is given by following Ampere's law. (Also known as
Ampere's Biot-Savart law),
F= (Ia cross r) cross Ib/r^3 ………………..2.
(Ia cross r)/r^3 gives magnetic field intensity B. It is in the
z direction. B is not a force vector, because actual force is in the x
direction. (For this reason B is not called force field, it is called
magnetic induction, whatever that may mean).
If we rotate Ib in the y-z plane, then the direction of the
force remains constant in x, always between the elements, but the
magnitude changes from maximum to zero, as Ib changes direction from y
to z respectively.
If we rotate Ib in the x-y plane, then the magnitude of the
force remains constant at maximum but the direction rotates along with
it. Direction of the force is x, when Ib is in the y direction and it
is y when Ib is in the x direction.
And here lies the problem!
If we consider magnetic field just a mathematical entity, same as
electric field, then we must always be able to look at the actual
sources of the force to explain it, Taking into consideration that the
currents are vectors, magnetic force may change in magnitude but never
in the direction. Therefore under all conditions, eq.1 alone should
have been found true. But it is true only as a special case, that when
Ib rotates in the y-z plane.
When the direction of Ib is x, the force exerted on Ib is
parallel to Ia. The force is no more 'between' the current elements
and so no more 'due' to the current elements.
Clearly in the above case, Ib is not responding directly to Ia;
it is responding to the B field of Ia and this is possible only if B
field is real.
Obviously Ib, too, has a real field and the actual mechanical
fore between the current elements is due to the interaction of these
real fields.
The picture of E vector lines is imaginary, which helps
visualization. Picture of circular B lines is not only not imaginary,
but it represents real physical entity. A third entity, after two
others, mass and charge.
Real: such as mass and charge
Intangible: such as force and energy
Fictitious: such as elctric field
-------------------------------------
This is one article out of a serial. New visitors should go through
all the previous. Dates are posting dates. Articles are posted to 1.
Alt.sci.physics.new-theories 2.Sci.physics 3.sci.physics.electromag
4. sci.physics.relativity
1. Limitation of Divergence theorem 8-3-04 1,2,3,4
2. Electron positron annihilation 12-3-04 1,2,3,4
3. Changing magnetic field does
not produce electric field 17-3-04 1,2,3,4
4. Barnett's experiment 22-3-04 1,2,3,4
5. Relativity and electrodynamics 25-3-04 1,2,3,4
6. Relativity of two moving charges 2-4-04 1,2,3,4
7. Relativity of steady charge and current 11-4-04 1,2,3,4
8 Relativity of two currents 14-4-04 1,2,3,4
9. Nature of electric field 16-4-04 1,2,3,4
10. Magnetic field is real 22-4-04 2,3,4
11. once more relativity 5-5-04 1,2,3,4
12. A new paradox in SR 10-5-04 1,2,3,4
.
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| User: "Bilge" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
17 May 2004 07:22:44 AM |
|
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V.K.Tamhane:
[...]
(Ia cross r)/r^3 gives magnetic field intensity B. It is in the
z direction. B is not a force vector, because actual force is in the x
direction. (For this reason B is not called force field, it is called
magnetic induction, whatever that may mean).
Magnetic fields don't change the energy of charged particles.
And here lies the problem!
More like, here lies your problem...
If we consider magnetic field just a mathematical entity, same as
electric field, then we must always be able to look at the actual
sources of the force to explain it,
And?
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current _densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
magnetic force may change in magnitude but never
in the direction. Therefore under all conditions, eq.1 alone should
have been found true. But it is true only as a special case, that when
Ib rotates in the y-z plane.
When the direction of Ib is x, the force exerted on Ib is
parallel to Ia. The force is no more 'between' the current elements
and so no more 'due' to the current elements.
It's completely inappropriate to consider the current elements outside
of the integral sign. Ampere's law does not permit you to do that.
Clearly in the above case, Ib is not responding directly to Ia;
it is responding to the B field of Ia and this is possible only if B
field is real.
Obviously Ib, too, has a real field and the actual mechanical
fore between the current elements is due to the interaction of these
real fields.
What is your deal with magnetic fields being ``real'' or not ``real''?
They are obviously real to the extent that I can measure something I
call a magnetic field. The fact that div B = 0 in maxwell's equations
tells you that there exists no source (or sink) for the magnetic field.
Feel free to change that. Maxwells equations may be rewritten
with complete symmetry between electric and magnetic fields,
complete with magnetic charges. Then there exists a relation
between the various quantities in those equations. For example:
q_e' = q_e cos(A) + q_m sin(A)
q_m' = q_m cos(A) - q_e sin(A)
etc., which allows you to transform those equations in anyway you
like by choosing the angle A. If the ration q_e/q_m is the same in
all matter, then you may _choose_ to eliminate either q_e or q_m.
For example, to eliminate magnetic charge,
q_m' = 0 = q_m cos(A) - q_e sin(A) ==> q_m = q_e tan(A)
q_e' = q_e cos(A) + q_e tan(A) sin(A) = q_e/cos^2(A)
Which just rescales the electric charge. In other words, what
we define as a magnetic field is convention, not necessity.
This is one article out of a serial. New visitors should go through
You can eliminate this article and the ``new paradox in SR''
from your list. When I see the rest, I'll eliminate those as well.
all the previous. Dates are posting dates. Articles are posted to 1.
Alt.sci.physics.new-theories 2.Sci.physics 3.sci.physics.electromag
4. sci.physics.relativity
1. Limitation of Divergence theorem 8-3-04 1,2,3,4
2. Electron positron annihilation 12-3-04 1,2,3,4
3. Changing magnetic field does
not produce electric field 17-3-04 1,2,3,4
4. Barnett's experiment 22-3-04 1,2,3,4
5. Relativity and electrodynamics 25-3-04 1,2,3,4
6. Relativity of two moving charges 2-4-04 1,2,3,4
7. Relativity of steady charge and current 11-4-04 1,2,3,4
8 Relativity of two currents 14-4-04 1,2,3,4
9. Nature of electric field 16-4-04 1,2,3,4
10. Magnetic field is real 22-4-04 2,3,4
11. once more relativity 5-5-04 1,2,3,4
12. A new paradox in SR 10-5-04 1,2,3,4
.
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| User: "Harold Ensle" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
18 May 2004 01:22:48 AM |
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"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
[...]
(Ia cross r)/r^3 gives magnetic field intensity B. It is in the
z direction. B is not a force vector, because actual force is in the x
direction. (For this reason B is not called force field, it is called
magnetic induction, whatever that may mean).
Magnetic fields don't change the energy of charged particles.
i.e Magnetic fields will do no work on a charged particle.
Since Tamhane did not say that they would, I don't know
why you posted this.
And here lies the problem!
More like, here lies your problem...
If we consider magnetic field just a mathematical entity, same as
electric field, then we must always be able to look at the actual
sources of the force to explain it,
And?
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current _densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry me.
Current is by definition a vector since it has a direction. (Is the
current going East...west...north..south....up....down...etc)
Your equation determines the _magnitude_ of current that
passes throught the surface. And yes, the _magnitude_
of current is a scalar.
magnetic force may change in magnitude but never
in the direction. Therefore under all conditions, eq.1 alone should
have been found true. But it is true only as a special case, that when
Ib rotates in the y-z plane.
When the direction of Ib is x, the force exerted on Ib is
parallel to Ia. The force is no more 'between' the current elements
and so no more 'due' to the current elements.
It's completely inappropriate to consider the current elements outside
of the integral sign. Ampere's law does not permit you to do that.
Clearly in the above case, Ib is not responding directly to Ia;
it is responding to the B field of Ia and this is possible only if B
field is real.
Obviously Ib, too, has a real field and the actual mechanical
fore between the current elements is due to the interaction of these
real fields.
What is your deal with magnetic fields being ``real'' or not ``real''?
I think he means does the magnetic field exist as a real property of
a space instead of merely mathematical book-keeping relating
to the interaction of separate particles.
They are obviously real to the extent that I can measure something I
call a magnetic field. The fact that div B = 0 in maxwell's equations
tells you that there exists no source (or sink) for the magnetic field.
Again irrelevant.
Feel free to change that. Maxwells equations may be rewritten
with complete symmetry between electric and magnetic fields,
You cannot have complete symmetry without a magnetic monopole.
So I assume you are beginning to babble here.......
[.........]
H.Ellis Ensle
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| User: "Bilge" |
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| Title: Re: Ampere's law proves reality of magnetic field |
18 May 2004 08:30:23 AM |
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Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current _densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry me.
Current is by definition a vector since it has a direction. (Is the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS = I
Your equation determines the _magnitude_ of current that passes throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law reads:
I dl x r, not dI x r.
magnetic force may change in magnitude but never
in the direction. Therefore under all conditions, eq.1 alone should
have been found true. But it is true only as a special case, that when
Ib rotates in the y-z plane.
When the direction of Ib is x, the force exerted on Ib is
parallel to Ia. The force is no more 'between' the current elements
and so no more 'due' to the current elements.
It's completely inappropriate to consider the current elements outside
of the integral sign. Ampere's law does not permit you to do that.
Clearly in the above case, Ib is not responding directly to Ia;
it is responding to the B field of Ia and this is possible only if B
field is real.
Obviously Ib, too, has a real field and the actual mechanical
fore between the current elements is due to the interaction of these
real fields.
What is your deal with magnetic fields being ``real'' or not ``real''?
I think he means does the magnetic field exist as a real property of
a space instead of merely mathematical book-keeping relating
to the interaction of separate particles.
What he means is his problem and it does appear to be some pet
problem of his.
They are obviously real to the extent that I can measure something I
call a magnetic field. The fact that div B = 0 in maxwell's equations
tells you that there exists no source (or sink) for the magnetic field.
Again irrelevant.
Harold, if all you are going to is make dumb comments, I'm simply
going to tell you that they're dumb. Of course it's relevant. How
can you have a field which is a field in its own right if there
exists no source of that field? The reason the B-field is considered
to be an artifact of a changing E-field, is because there is
no source for the B-field other than a changing E-field.
Feel free to change that. Maxwells equations may be rewritten
with complete symmetry between electric and magnetic fields,
You cannot have complete symmetry without a magnetic monopole.
It's not worth repeating this until you get it, since I've posted
it before. Go look in jackson instead of posting uninformed *****.
You'll find the details to what you snipped just before the section
on monopoles.
So I assume you are beginning to babble here.......
If you could have understood what you snipped, you would
have seen your comment above was the result of your own ignorance.
.
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| User: "Harry" |
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| Title: Re: Ampere's law proves reality of magnetic field |
19 May 2004 05:21:56 AM |
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"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry me.
Current is by definition a vector since it has a direction. (Is the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS = I
Your equation determines the _magnitude_ of current that passes throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism) treats "I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.) treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it can be
presented as a vector.
Maybe a little sloppy, but very handy!
Harald
.
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| User: "Bilge" |
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| Title: Re: Ampere's law proves reality of magnetic field |
19 May 2004 01:48:08 PM |
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Harry:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Scalars do not have directions. Note that the bio-savart law reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism) treats "I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.) treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it can be
presented as a vector. Maybe a little sloppy, but very handy!
I's a question of physics, not (somewhat dubious) notational convenience.
.
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| User: "Bill Hobba" |
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| Title: Re: Ampere's law proves reality of magnetic field |
19 May 2004 05:41:15 PM |
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"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncancl5.44m.dubious@radioactivex.lebesque-al.net...
Harry:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Scalars do not have directions. Note that the bio-savart law reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism) treats
"I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it can be
presented as a vector. Maybe a little sloppy, but very handy!
I's a question of physics, not (somewhat dubious) notational
convenience.
Agreed. There is no doubt that I is a scalar and represents the charge
traveling though a surface. I have a number of EM books and it is only
Griffith that does not make it clear what it is. The two most authoritative
sources I have (if it is authority your after - I agree with Bilge it is a
matter of physics not authority) are Landau -The Classical Theory of Fields
and The Feynman Lectures - both define it correctly.
Thanks
Bill
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| User: "Franz Heymann" |
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| Title: Re: Ampere's law proves reality of magnetic field |
20 May 2004 03:17:34 PM |
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"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry
me.
Current is by definition a vector since it has a direction. (Is
the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS = I
Your equation determines the _magnitude_ of current that passes
throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law
reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism)
treats "I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
It is unnscessary to report here that an idiot called Day wrote a book
for undereducating engineers in the customary fachion.
When a current has one single direction as well as a magnitude it
can be
presented as a vector.
A current can flow round a corner. A current can be extended in
space.
Maybe a little sloppy, but very handy!
Extremely sloppy and a dead end.
Franz
.
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| User: "V.K.Tamhane" |
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| Title: Re: Ampere's law proves reality of magnetic field |
21 May 2004 02:00:59 AM |
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"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message news:<c8j3ot$rpa$11@titan.btinternet.com>...
(Intro to vector analysis for Radio and electronic eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
It is unnscessary to report here that an idiot called Day wrote a book
for undereducating engineers in the customary fachion.
When a current has one single direction as well as a magnitude it
can be
presented as a vector.
A current can flow round a corner. A current can be extended in
space.
Maybe a little sloppy, but very handy!
Extremely sloppy and a dead end.
Franz
Franz, you have learned your physics by rote. You don't
have any concepts, no power to visualize. You are just a living
encyclopedia, a hard disc of a computer, which cannot think. You make
much ado about nothing
But this is a small part of the big game. You are no doubt
a member of a barking brigade of physics Al-Quida. One who cannot
tolerate attack on established theories, which you have memorized
without thinking. Unmoderated physics newsgroup is the only voice of
freedom, against the stinking gutter of mathematical abstractions and
that is what you can't bear. Once these newsgroups become a platform
for expletives then they shall die a quiet death and monkey
mathematicians like you would peacefully indulge in the disgusting
concept less acrobatics, audaciously called physics.
.
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| User: "Harold Ensle" |
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| Title: Re: Ampere's law proves reality of magnetic field |
19 May 2004 02:38:00 PM |
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"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry me.
Current is by definition a vector since it has a direction. (Is the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS = I
Your equation determines the _magnitude_ of current that passes
throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism) treats "I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it can be
presented as a vector.
Maybe a little sloppy, but very handy!
NO. Current is always a vector by physical definition. It has a
direction therefore it is a vector. ANY equation that yields
a scalar value for a current is, in fact, yielding the magnitude
of the current.
This is not a grey area in physics. This is a basic fundamental
physics definition which if one is not clear about it, one needs
to review.
The fact that people are using various equations to try and
show whether it is a vector or not is completely ridiculous.
An equation does not have to give the vector. It could yield
the magnitude, or just the direction, or just a component...all
depending on the particular equation and its purpose.
H.Ellis Ensle
.
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| User: "Franz Heymann" |
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| Title: Re: Ampere's law proves reality of magnetic field |
20 May 2004 03:17:35 PM |
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"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in
message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_.
Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that
worry me.
Current is by definition a vector since it has a direction.
(Is the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS =
I
Your equation determines the _magnitude_ of current that
passes
throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law
reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism)
treats "I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic
eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it
can be
presented as a vector.
Maybe a little sloppy, but very handy!
NO. Current is always a vector by physical definition.
No. Current is the integral over a surface of the quantity J dot ds,
where J is the current density vector and ds is a vecror surface
element. A dot product is a scalar quantity.
It has a
direction therefore it is a vector.
No. What is the direction of a current flowing from a cylindrical
electrode in an electrolytic cell?
And when answering, don't tell me what the direction of the current
density is.
ANY equation that yields
a scalar value for a current is, in fact, yielding the magnitude
of the current.
A current, by virtue of its definition, is a scalar quantity and has
no direction associated with it, other than that which might be
conferred by an algebraic sign.
This is not a grey area in physics.
Correct.
This is a basic fundamental
physics definition which if one is not clear about it, one needs
to review.
If you had carried out your own recommendation, you would have made
less of an arse of yourself.
The fact that people are using various equations to try and
show whether it is a vector or not is completely ridiculous.
It is not a question of various equations. It is a matter of
definition.
From its definition, it is clear that it is a scalar.
An equation does not have to give the vector.
What does one have to do to an equation to make it give the vector?
It could yield
the magnitude, or just the direction, or just a component...all
depending on the particular equation and its purpose.
Arses are distinguishable from elbows by most, but not you.
Franz
.
|
|
|
| User: "Creighton Hogg" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
20 May 2004 04:18:48 PM |
|
|
On Thu, 20 May 2004, Franz Heymann wrote:
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
An equation does not have to give the vector.
What does one have to do to an equation to make it give the vector?
Take it our for dinner and a movie?
.
|
|
|
| User: "Franz Heymann" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
22 May 2004 02:27:11 PM |
|
|
"Creighton Hogg" <wchogg@hep.wisc.edu> wrote in message
news:Pine.LNX.4.44.0405201616530.3964-100000@azalea.hep.wisc.edu...
On Thu, 20 May 2004, Franz Heymann wrote:
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
An equation does not have to give the vector.
What does one have to do to an equation to make it give the
vector?
Take it our for dinner and a movie?
{:-))
Franz
.
|
|
|
|
| User: "Dirk Van de moortel" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
20 May 2004 04:48:03 PM |
|
|
"Creighton Hogg" <wchogg@hep.wisc.edu> wrote in message news:Pine.LNX.4.44.0405201616530.3964-100000@azalea.hep.wisc.edu...
On Thu, 20 May 2004, Franz Heymann wrote:
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
An equation does not have to give the vector.
What does one have to do to an equation to make it give the vector?
Take it our for dinner and a movie?
ahhh!
Good one! :-D
Dirk Vdm
.
|
|
|
| User: "Bilge" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
21 May 2004 12:18:07 AM |
|
|
Dirk Van de moortel:
"Creighton Hogg" <wchogg@hep.wisc.edu> wrote in message news:Pine.LNX.4.44.0405201616530.3964-100000@azalea.hep.wisc.edu...
On Thu, 20 May 2004, Franz Heymann wrote:
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
An equation does not have to give the vector.
What does one have to do to an equation to make it give the vector?
Take it our for dinner and a movie?
ahhh!
Good one! :-D
Maybe harold will even accept that answer, since it doesn't rely too
much on higher arithmetic.
.
|
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|
|
|
|
|
| User: "Bill Hobba" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
19 May 2004 05:50:36 PM |
|
|
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry me.
Current is by definition a vector since it has a direction. (Is the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS = I
Your equation determines the _magnitude_ of current that passes
throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism) treats
"I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it can be
presented as a vector.
Maybe a little sloppy, but very handy!
NO. Current is always a vector by physical definition. It has a
direction therefore it is a vector.
No Harold. Have a look at the Feynman Lectures on Physics Chapter 13 volume
2. It is a scalar and represents the charge flowing across a surface in a
unit time. The fact some authors express it badly will not change the
physics which is I = integral J.da where J is the current density. This
means I must be a scalar. Griffith gets around his bad definition by
defining the density as I/da from his definition of I = y.V. This is
probably to get around having to define the current density before the
current - but is still bad physics.
Thanks
Bill
ANY equation that yields
a scalar value for a current is, in fact, yielding the magnitude
of the current.
This is not a grey area in physics. This is a basic fundamental
physics definition which if one is not clear about it, one needs
to review.
The fact that people are using various equations to try and
show whether it is a vector or not is completely ridiculous.
An equation does not have to give the vector. It could yield
the magnitude, or just the direction, or just a component...all
depending on the particular equation and its purpose.
H.Ellis Ensle
.
|
|
|
| User: "Harold Ensle" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
20 May 2004 10:19:16 AM |
|
|
"Bill Hobba" <bhobba@hotmail.com> wrote in message
news:0xRqc.48325$TT.35149@news-server.bigpond.net.au...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry
me.
Current is by definition a vector since it has a direction. (Is
the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS = I
Your equation determines the _magnitude_ of current that passes
throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law
reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism) treats
"I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it can
be
presented as a vector.
Maybe a little sloppy, but very handy!
NO. Current is always a vector by physical definition. It has a
direction therefore it is a vector.
No Harold. Have a look at the Feynman Lectures on Physics Chapter 13
volume
2. It is a scalar and represents the charge flowing across a surface in a
unit time. The fact some authors express it badly will not change the
physics which is I = integral J.da where J is the current density. This
means I must be a scalar.
No it doesn't! The equation only yields the current that passes
through a pre-chosen surface, thus it is selecting the component
of current which is normal to the surface. And since the direction
is restricted it yields a scalar, which in this case is the magnitude
of the component of the current _vector_ normal to the surface.
As I explained above (and you failed to understand), this equation
tells you nothing about the current's actual vector nature.
Griffith gets around his bad definition by
defining the density as I/da from his definition of I = y.V. This is
probably to get around having to define the current density before the
current - but is still bad physics.
No it is good physics as J=I/da is the correct (and obvious) relation
between current density and current.
The fact that you don't realize it is telling indeed.
H.Ellis Ensle
.
|
|
|
| User: "Franz Heymann" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
21 May 2004 03:42:19 PM |
|
|
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:U%3rc.3433$be.459@newsread2.news.pas.earthlink.net...
"Bill Hobba" <bhobba@hotmail.com> wrote in message
news:0xRqc.48325$TT.35149@news-server.bigpond.net.au...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in
message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in
message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are
vectors,
Currents are _NOT_ vectors. Currents are _scalars_.
Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that
worry
me.
Current is by definition a vector since it has a
direction. (Is
the
current going
East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J .
dS = I
Your equation determines the _magnitude_ of current that
passes
throught
the surface. And yes, the _magnitude_ of current is a
scalar.
Scalars do not have directions. Note that the bio-savart
law
reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2
(Electromagnetism) treats
"I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic
eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude
it can
be
presented as a vector.
Maybe a little sloppy, but very handy!
NO. Current is always a vector by physical definition. It has a
direction therefore it is a vector.
No Harold. Have a look at the Feynman Lectures on Physics Chapter
13
volume
2. It is a scalar and represents the charge flowing across a
surface in a
unit time. The fact some authors express it badly will not change
the
physics which is I = integral J.da where J is the current density.
This
means I must be a scalar.
No it doesn't! The equation only yields the current that passes
through a pre-chosen surface, thus it is selecting the component
of current which is normal to the surface.
You have the intellect of a ten year old. Are you a ten year old? Do
you wear long pants yet?
Go and learn some very elementary vector algebra and don't speak such
awful rubbish.
And since the direction
is restricted it yields a scalar, which in this case is the
magnitude
of the component of the current _vector_ normal to the surface.
As I explained above (and you failed to understand), this equation
tells you nothing about the current's actual vector nature.
Balls.
Griffith gets around his bad definition by
defining the density as I/da from his definition of I = y.V. This
is
probably to get around having to define the current density before
the
current - but is still bad physics.
No it is good physics as J=I/da is the correct (and obvious)
relation
between current density and current.
That is the approach of an ill-educated (or should I say "trained")
engineer. It is also incorrect, since there is no vector operation
corresponding to a division.
The fact that you don't realize it is telling indeed.
What is even more telling is that you are not ashamed of committing
your crap to the google archives.
Franz
.
|
|
|
| User: "Harold Ensle" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
22 May 2004 09:08:16 AM |
|
|
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message
news:c8lpja$k57$6@sparta.btinternet.com...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:U%3rc.3433$be.459@newsread2.news.pas.earthlink.net...
[.................]
No it doesn't! The equation only yields the current that passes
through a pre-chosen surface, thus it is selecting the component
of current which is normal to the surface.
You have the intellect of a ten year old. Are you a ten year old? Do
you wear long pants yet?
Go and learn some very elementary vector algebra and don't speak such
awful rubbish.
You are a lot more stupid than I ever realized. Truely amazing!
And since the direction
is restricted it yields a scalar, which in this case is the
magnitude
of the component of the current _vector_ normal to the surface.
As I explained above (and you failed to understand), this equation
tells you nothing about the current's actual vector nature.
Balls.
No...it is simply true.
Griffith gets around his bad definition by
defining the density as I/da from his definition of I = y.V. This
is
probably to get around having to define the current density before
the
current - but is still bad physics.
No it is good physics as J=I/da is the correct (and obvious)
relation
between current density and current.
That is the approach of an ill-educated (or should I say "trained")
engineer. It is also incorrect, since there is no vector operation
corresponding to a division.
Well. since I am dividing by a scalar, that wouldn't be a problem
would it?
LOL
[...]
H.Ellis Ensle
.
|
|
|
| User: "Franz Heymann" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
23 May 2004 12:55:29 AM |
|
|
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:k9Jrc.5773$be.595@newsread2.news.pas.earthlink.net...
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message
news:c8lpja$k57$6@sparta.btinternet.com...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:U%3rc.3433$be.459@newsread2.news.pas.earthlink.net...
[.................]
No it doesn't! The equation only yields the current that passes
through a pre-chosen surface, thus it is selecting the component
of current which is normal to the surface.
You have the intellect of a ten year old. Are you a ten year old?
Do
you wear long pants yet?
Go and learn some very elementary vector algebra and don't speak
such
awful rubbish.
You are a lot more stupid than I ever realized. Truely amazing!
And since the direction
is restricted it yields a scalar, which in this case is the
magnitude
of the component of the current _vector_ normal to the surface.
As I explained above (and you failed to understand), this
equation
tells you nothing about the current's actual vector nature.
Balls.
No...it is simply true.
Griffith gets around his bad definition by
defining the density as I/da from his definition of I = y.V.
This
is
probably to get around having to define the current density
before
the
current - but is still bad physics.
No it is good physics as J=I/da is the correct (and obvious)
relation
between current density and current.
That is the approach of an ill-educated (or should I say
"trained")
engineer. It is also incorrect, since there is no vector
operation
corresponding to a division.
Well. since I am dividing by a scalar, that wouldn't be a problem
would it?
You are doing nothing of the kind
Franz
.
|
|
|
|
|
|
| User: "Bill Hobba" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
20 May 2004 06:38:13 PM |
|
|
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:U%3rc.3433$be.459@newsread2.news.pas.earthlink.net...
"Bill Hobba" <bhobba@hotmail.com> wrote in message
news:0xRqc.48325$TT.35149@news-server.bigpond.net.au...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_. Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that worry
me.
Current is by definition a vector since it has a direction. (Is
the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS = I
Your equation determines the _magnitude_ of current that passes
throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law
reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism)
treats
"I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it
can
be
presented as a vector.
Maybe a little sloppy, but very handy!
NO. Current is always a vector by physical definition. It has a
direction therefore it is a vector.
No Harold. Have a look at the Feynman Lectures on Physics Chapter 13
volume
2. It is a scalar and represents the charge flowing across a surface in
a
unit time. The fact some authors express it badly will not change the
physics which is I = integral J.da where J is the current density. This
means I must be a scalar.
No it doesn't! The equation only yields the current that passes
through a pre-chosen surface, thus it is selecting the component
of current which is normal to the surface. And since the direction
is restricted it yields a scalar, which in this case is the magnitude
of the component of the current _vector_ normal to the surface.
As I explained above (and you failed to understand), this equation
tells you nothing about the current's actual vector nature.
What are you arguing - that definition does not make it a scalar? If so
learn some vector algebra - see the . between J and da that is called the
dot product and takes two vectors and gives a scalar. Since your so fond of
your hero Griffith have a look at page 31 of his book. OTOH if your arguing
that definition is incorrect then ague it with the authors of the many
textbooks that define it that way. Griffith is the only one that does not.
Griffith gets around his bad definition by
defining the density as I/da from his definition of I = y.V. This is
probably to get around having to define the current density before the
current - but is still bad physics.
No it is good physics as J=I/da is the correct (and obvious) relation
between current density and current.
The fact that you don't realize it is telling indeed.
The fact that other authors disagree with you is even more telling and
trivially disproves your assertion 'No it is good physics as J=I/da is the
correct (and obvious) relation between current density and current'. If it
was so obvious then everyone else would not have fallen for it. To claim
you (and Griffith) are the only ones in the world that is correct and
everyone else is wrong, even great physicists like Feynman, is a sign of
something that occurs only too frequently on this forum and needs to be
treated by a professional. The maximum you can claim from all of this is
that you have one author that agrees with you and you prefer his definition
not that everyone else is obviously wrong. And even if you are correct and
you use the definitions of Griffith you do not get F=(Ia) dot (Ib)/r^2 (as
the original poster asserted) as the force between two current carrying
wires - see equation 5.33 on page 210. Or is Griffith wrong here but
correct everywhere else? Again look at what the original poster asserted
was amperes law F= (Ia cross r) cross Ib/r^3 and compare that with equation
5.48 from Griffiths. So exactly what is your saying Harald - the original
poster is correct or incorrect?
Thanks
Bill
.
|
|
|
| User: "Harold Ensle" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
21 May 2004 01:48:41 AM |
|
|
"Bill Hobba" <bhobba@hotmail.com> wrote in message
news:Fjbrc.50674$TT.38354@news-server.bigpond.net.au...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:U%3rc.3433$be.459@newsread2.news.pas.earthlink.net...
"Bill Hobba" <bhobba@hotmail.com> wrote in message
news:0xRqc.48325$TT.35149@news-server.bigpond.net.au...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in
message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are vectors,
Currents are _NOT_ vectors. Currents are _scalars_.
Current
_densities_
are vectors and a current is the surface integral of J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors that
worry
me.
Current is by definition a vector since it has a direction.
(Is
the
current going East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law reads:
curl B = J => \integral (curl B) . dS = \integral J . dS =
I
Your equation determines the _magnitude_ of current that
passes
throught
the surface. And yes, the _magnitude_ of current is a scalar.
Scalars do not have directions. Note that the bio-savart law
reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2 (Electromagnetism)
treats
"I"
as only a scalar.
But W.D.Day (Intro to vector analysis for Radio and electronic
eng.)
treats
"I" as a vector and writes:
F = I x B (he apparently took l=1).
When a current has one single direction as well as a magnitude it
can
be
presented as a vector.
Maybe a little sloppy, but very handy!
NO. Current is always a vector by physical definition. It has a
direction therefore it is a vector.
No Harold. Have a look at the Feynman Lectures on Physics Chapter 13
volume
2. It is a scalar and represents the charge flowing across a surface
in
a
unit time. The fact some authors express it badly will not change the
physics which is I = integral J.da where J is the current density.
This
means I must be a scalar.
No it doesn't! The equation only yields the current that passes
through a pre-chosen surface, thus it is selecting the component
of current which is normal to the surface. And since the direction
is restricted it yields a scalar, which in this case is the magnitude
of the component of the current _vector_ normal to the surface.
As I explained above (and you failed to understand), this equation
tells you nothing about the current's actual vector nature.
What are you arguing - that definition does not make it a scalar?
The equation is NOT the definition of current. It is an equation that
tells you the magnitude of current passing through a particular surface.
If so
learn some vector algebra - see the . between J and da that is called the
dot product and takes two vectors and gives a scalar.
I never said otherwise so this is irrelevant.
Since your so fond of
your hero Griffith have a look at page 31 of his book.
Nothing seemed to be relevant there.
OTOH if your arguing
that definition is incorrect then ague it with the authors of the many
textbooks that define it that way. Griffith is the only one that does
not.
What a ridiculous statement. Have you read all E&M textbooks?
How could you possibly know that he is the only one?
This is just an example of your sloppy reasoning.
Griffith gets around his bad definition by
defining the density as I/da from his definition of I = y.V. This is
probably to get around having to define the current density before the
current - but is still bad physics.
No it is good physics as J=I/da is the correct (and obvious) relation
between current density and current.
The fact that you don't realize it is telling indeed.
The fact that other authors disagree with you is even more telling and
trivially disproves your assertion 'No it is good physics as J=I/da is
the
correct (and obvious) relation between current density and current'. If
it
was so obvious then everyone else would not have fallen for it. To claim
you (and Griffith) are the only ones in the world that is correct and
everyone else is wrong, even great physicists like Feynman, is a sign of
something that occurs only too frequently on this forum and needs to be
treated by a professional. The maximum you can claim from all of this is
that you have one author that agrees with you and you prefer his
definition
not that everyone else is obviously wrong. And even if you are correct
and
you use the definitions of Griffith you do not get F=(Ia) dot (Ib)/r^2
(as
the original poster asserted) as the force between two current carrying
wires - see equation 5.33 on page 210. Or is Griffith wrong here but
correct everywhere else? Again look at what the original poster asserted
was amperes law F= (Ia cross r) cross Ib/r^3 and compare that with
equation
5.48 from Griffiths. So exactly what is your saying Harald - the original
poster is correct or incorrect?
Actually I never really read his post. I just notice the strange belief
from several posters that current was a scalar.
But now that you brought it up...I went to the trouble to look at his
post and yes...Tamhane's equations are correct (though the explanation and
notation could be clearer perhaps). His first equation above is a special
case of the second equation. Here is how you would derive it:
The magnetic field from a current element is given by:
dB=(Ia cross r)/r^3 dl (Griffith's page 208 except different units
with mu/4*pi dropped and the full r vector is used on top instead
of the unit vector).
One can just as easily write this as:
dB=(dIa cross r)/r^3 (using a differential of current)
The force on a current element in a magnetic field is given by:
dF=J cross B dV (Griffith's page 205)
We can write dF=J cross B dAdl where dA is perpendicular to J
then dF=Ib cross B dl which we can convert as above to the
differential of current yielding:
dF=dIb cross B
Then we substitute for B and get:
dF=dIb cross (dIa cross r)/r^3 (Tamhane's 2nd equation)
Using an identity yields:
dF=(dIa(dIb dot r)-r(dIa dot dIb))/r^3
Note that if the currents remain in parallel _planes_ (here Tamhane
misspoke as he stated parallel currents) dlB dot r=0 and you have:
dF=-(dIa dot dIb)/r^2 (Tamhane's 1st equation.....with minus sign)
How easy was that?
H.Ellis Ensle
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| User: "Bilge" |
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| Title: Re: Ampere's law proves reality of magnetic field |
21 May 2004 03:50:13 PM |
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Harold Ensle:
Then we substitute for B and get:
dF=dIb cross (dIa cross r)/r^3 (Tamhane's 2nd equation)
Using an identity yields:
dF=(dIa(dIb dot r)-r(dIa dot dIb))/r^3
Note that if the currents remain in parallel _planes_ (here Tamhane
misspoke as he stated parallel currents) dlB dot r=0 and you have:
dF=-(dIa dot dIb)/r^2 (Tamhane's 1st equation.....with minus sign)
But you cannot obtain a physical quantity without integrating out
the fiction you've employed to write (I_a I_b) dl_a . dl_b as
dI_a . dI_b. Griffiths gives an example of such a mistake where
he shows that you cannot obtain the magnetic field of a point charge
by taking I = qv.
.
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| User: "Harold Ensle" |
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| Title: Re: Ampere's law proves reality of magnetic field |
22 May 2004 09:49:06 AM |
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"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncassi4.hae.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
Then we substitute for B and get:
dF=dIb cross (dIa cross r)/r^3 (Tamhane's 2nd equation)
Using an identity yields:
dF=(dIa(dIb dot r)-r(dIa dot dIb))/r^3
Note that if the currents remain in parallel _planes_ (here Tamhane
misspoke as he stated parallel currents) dlB dot r=0 and you have:
dF=-(dIa dot dIb)/r^2 (Tamhane's 1st equation.....with minus sign)
But you cannot obtain a physical quantity without integrating out
the fiction you've employed to write (I_a I_b) dl_a . dl_b as
dI_a . dI_b.
Yes...you would have to perform an integral to obtain a practical result.
But the formula is no more a fiction than any other differential formula.
Griffiths gives an example of such a mistake
No...this is something different.
where
he shows that you cannot obtain the magnetic field of a point charge
by taking I = qv.
Of course...it isn't even the right units. Griffith's (correct) definition
of current is I= lambda*v where lambda is the linear charge density.
When dealing with a single charge, the linear charge density is not
known. And whether using Tamhane's method or the usual methods,
a single charge requires a special treatment anyway.
But the differential formula given by Tamhane is correct and
could be used to solve a real problem such as the force between
two parallel infinitely long conductors (with current).
H.Ellis Ensle
.
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| User: "Bilge" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
22 May 2004 01:32:18 PM |
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|
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncassi4.hae.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
Then we substitute for B and get:
dF=dIb cross (dIa cross r)/r^3 (Tamhane's 2nd equation)
Using an identity yields:
dF=(dIa(dIb dot r)-r(dIa dot dIb))/r^3
Note that if the currents remain in parallel _planes_ (here Tamhane
misspoke as he stated parallel currents) dlB dot r=0 and you have:
dF=-(dIa dot dIb)/r^2 (Tamhane's 1st equation.....with minus sign)
But you cannot obtain a physical quantity without integrating out
the fiction you've employed to write (I_a I_b) dl_a . dl_b as
dI_a . dI_b.
Yes...you would have to perform an integral to obtain a practical result.
No, you have to perform the integral to obtain a mathematically valid
result, since stokes theorem is used to obtain that expression and
stokes theorem requires integrating around the boundary of the area
inside the integral of (curl J) . dS.
But the formula is no more a fiction than any other differential formula.
Yes, it is, since even the concept of a ``piece'' of a current is
incorrect as it violates conservation of charge unless the loop is closed.
Griffiths gives an example of such a mistake
No...this is something different.
No, it isn't something different.
where
he shows that you cannot obtain the magnetic field of a point charge
by taking I = qv.
Of course...it isn't even the right units. Griffith's (correct) definition
of current is I= lambda*v where lambda is the linear charge density.
I've already explained that using such a definition means your
current has the electric field of a (moving) line charge and
since a current in a wire has no electric field, that cannot be
the correct definition of a current in a wire.
When dealing with a single charge, the linear charge density is not
known. And whether using Tamhane's method or the usual methods,
a single charge requires a special treatment anyway.
Why should that be unless there is something wrong with the
definitions you are trying to use?
But the differential formula given by Tamhane is correct and
could be used to solve a real problem such as the force between
two parallel infinitely long conductors (with current).
The correct way is no more difficult and it emphasizes the
correct physics.
.
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| User: "Harold Ensle" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
22 May 2004 03:13:43 PM |
|
|
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncav8rl.hae.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncassi4.hae.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
Then we substitute for B and get:
dF=dIb cross (dIa cross r)/r^3 (Tamhane's 2nd equation)
Using an identity yields:
dF=(dIa(dIb dot r)-r(dIa dot dIb))/r^3
Note that if the currents remain in parallel _planes_ (here Tamhane
misspoke as he stated parallel currents) dlB dot r=0 and you have:
dF=-(dIa dot dIb)/r^2 (Tamhane's 1st equation.....with minus sign)
But you cannot obtain a physical quantity without integrating out
the fiction you've employed to write (I_a I_b) dl_a . dl_b as
dI_a . dI_b.
Yes...you would have to perform an integral to obtain a practical
result.
No, you have to perform the integral to obtain a mathematically valid
result, since stokes theorem is used to obtain that expression and
stokes theorem requires integrating around the boundary of the area
inside the integral of (curl J) . dS.
But the formula is no more a fiction than any other differential
formula.
Yes, it is, since even the concept of a ``piece'' of a current is
incorrect as it violates conservation of charge unless the loop is closed.
Yes but this formula will give the correct forces related to that "piece".
Nobody is saying that such a piece can exist in isolation. Tamhane
is simply using this to make a very interesting point about how the
magnetic force relates to its source.
Griffiths gives an example of such a mistake
No...this is something different.
No, it isn't something different.
where
he shows that you cannot obtain the magnetic field of a point charge
by taking I = qv.
Of course...it isn't even the right units. Griffith's (correct)
definition
of current is I= lambda*v where lambda is the linear charge density.
I've already explained that using such a definition means your
current has the electric field of a (moving) line charge and
since a current in a wire has no electric field, that cannot be
the correct definition of a current in a wire.
Yes it can! Are you claiming that a wire can't have a moving
charge density?? To use the above definition for a wire, one
would simply use the drift velocity of the electrons in the wire.
When dealing with a single charge, the linear charge density is not
known. And whether using Tamhane's method or the usual methods,
a single charge requires a special treatment anyway.
Why should that be unless there is something wrong with the
definitions you are trying to use?
One does not use current density methods with a single
charge...period. You don't know that?
But the differential formula given by Tamhane is correct and
could be used to solve a real problem such as the force between
two parallel infinitely long conductors (with current).
The correct way is no more difficult and it emphasizes the
correct physics.
Tamhanes physics here is perfectly correct...............
However my derivation here sucks..........
My conversion from Idl to dI was total nonsense as it
changes the units of the problem....and I substituted
a dB for a B.
I am starting a new thread with the correct derivation.
H.Ellis Ensle
.
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| User: "Franz Heymann" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
23 May 2004 12:55:28 AM |
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|
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:CLJrc.5816$be.4075@newsread2.news.pas.earthlink.net...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncassi4.hae.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
Then we substitute for B and get:
dF=dIb cross (dIa cross r)/r^3 (Tamhane's 2nd equation)
Using an identity yields:
dF=(dIa(dIb dot r)-r(dIa dot dIb))/r^3
Note that if the currents remain in parallel _planes_ (here
Tamhane
misspoke as he stated parallel currents) dlB dot r=0 and you
have:
dF=-(dIa dot dIb)/r^2 (Tamhane's 1st equation.....with minus
sign)
But you cannot obtain a physical quantity without integrating
out
the fiction you've employed to write (I_a I_b) dl_a . dl_b as
dI_a . dI_b.
Yes...you would have to perform an integral to obtain a practical
result.
But the formula is no more a fiction than any other differential
formula.
Griffiths gives an example of such a mistake
No...this is something different.
where
he shows that you cannot obtain the magnetic field of a point
charge
by taking I = qv.
Of course...it isn't even the right units. Griffith's (correct)
definition
of current is I= lambda*v where lambda is the linear charge
density.
When dealing with a single charge, the linear charge density is not
known.
I know it. It is a delta function. Do you not know that?
And whether using Tamhane's method or the usual methods,
a single charge requires a special treatment anyway.
But the differential formula given by Tamhane is correct and
could be used to solve a real problem such as the force between
two parallel infinitely long conductors (with current).
It might be good enough for an engineer working in a narrow field
only. It is certainly not of general applicability.
Franz
.
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| User: "Franz Heymann" |
|
| Title: Re: Ampere's law proves reality of magnetic field |
22 May 2004 02:27:11 PM |
|
|
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:dDhrc.3446$Tn6.90@newsread1.news.pas.earthlink.net...
"Bill Hobba" <bhobba@hotmail.com> wrote in message
news:Fjbrc.50674$TT.38354@news-server.bigpond.net.au...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:U%3rc.3433$be.459@newsread2.news.pas.earthlink.net...
"Bill Hobba" <bhobba@hotmail.com> wrote in message
news:0xRqc.48325$TT.35149@news-server.bigpond.net.au...
"Harold Ensle" <heensle@ix.netcom.com> wrote in message
news:sIOqc.2542$be.818@newsread2.news.pas.earthlink.net...
"Harry" <harald.vanlintel@epfl.ch> wrote in message
news:40ab3499$1@epflnews.epfl.ch...
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in
message
news:slrncak5l9.44m.dubious@radioactivex.lebesque-al.net...
Harold Ensle:
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote
in
message
news:slrncahdac.5j.dubious@radioactivex.lebesque-al.net...
V.K.Tamhane:
Taking into consideration that the currents are
vectors,
Currents are _NOT_ vectors. Currents are
_scalars_.
Current
_densities_
are vectors and a current is the surface integral of
J,
I = \integral J . dS Note the scalar product.
Whoooo.....this is one of those basic physics errors
that
worry
me.
Current is by definition a vector since it has a
direction.
(Is
the
current going
East...west...north..south....up....down...etc)
Wrong. Current is a scalar. Note that ampere's law
reads:
curl B = J => \integral (curl B) . dS = \integral
J . dS =
I
Your equation determines the _magnitude_ of current
that
passes
throught
the surface. And yes, the _magnitude_ of current is a
scalar.
Scalars do not have directions. Note that the
bio-savart law
reads:
I dl x r, not dI x r.
SNIP
Bilge, indeed for example Alonso&Finn part 2
(Electromagnetism)
treats
"I"
as only a scalar.
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