1. Magnetic field of a moving charge is magnetic monopole.

Monopole? (left), Dipole (right)

Why would anyone expect magnetic monopoles would be some new type of particles?

Magnetic fields are only an effect of motion of electric fields i.e. electric charges - electrons and positrons.

Charge spin produces magnetic dipole moment, and these two poles are not two new "magnetic particles", just two additional fields, and only one particle, one charge, is "producing" all these fields.

Another kind of motion, next to spin, is spatial displacement, be it along a straight line or circular, it again produces yet another magnetic field. However, as it happens, different kinds of motion produce different kinds of magnetic fields. This magnetic field of a moving charge is monopole, I tell you, where this one pole is where magnetic field is strongest, the charge itself.

Somehow, everyone fails to recognize this magnetic monopole because of magnetic field lines, forgetting that magnetic force is perpendicular to magnetic field, so at the end magnetic force-lines, not field-liens, do converge into this monopole. Yes, no?

2.

3. The divergence of the magnetic field is actually zero in your case, and this means that there are no monopoles there. In your picture, you have shown a cross-section of the magnetic field of a moving charge. Again... No monopoles.

What you are calling a monopole is not a monopole at all... mostly since it does not act as a source or a sink of either electric nor magnetic field. The field lines neither originate nor end on the object, but instead they form a closed loop. That is a fatal flaw in your approach (you seem to be thinking that this closed loop somehow originates and ends, when it is, in fact, continuous).

The circular magnetic field lines you show actually have both a magnetic field line entering and leaving each point. Once you see that, you can see clearly that it means what you've shown cannot be a monopole. AFAICT, you are looking at the field after it's been transformed into a moving frame (the behavior in a moving frame and a rest frame are not the same), and all you really have there is a loop of wire with a current passing through it... aka a dipole.

The most likely explanation here is that you are defining "monopole" differently than it is defined in the physics community. That's simple enough to correct though, so good luck.

4. Originally Posted by inow
The divergence of the magnetic field is actually zero in your case, and this means that there are no monopoles there.
Where did you get your definition from?

Monopole means one pole. Dipole means two poles. Ok?

The direction of magnetic force is not the direction of magnetic field. The direction of magnetic field-lines has nothing to do with number of poles. Pole is the place of origin of magnetic field, the place from where its magnitude drops off by 1/r^2 if it is monopole, the point where the field is strongest. Yes?

Divergence
http://en.wikipedia.org/wiki/Divergence
- "In vector calculus, divergence is an operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar... More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point."

So, where do you see divergence is zero? Magnitude does diverge towards the pole with 1/r^2. Direction of the field is irrelevant, divergence is defined with signed scalars, plus the direction of magnetic force-lines, not field-lines, do point towards the pole.

Originally Posted by inow
In your picture, you have shown a cross-section of the magnetic field of a moving charge. Again... No monopoles.
How many poles does it have then?

What else do you want me to show you? Look at this:

This shows the field around two wires, side by side, that are carrying current in opposite directions.

This shows the field lines around a disk magnet where the North pole is at the top.

This shows magnetic strength of the disk magnet, strongest in the corners, not in the center of the poles.

You see how FIELD-lines do not correspond to FORCE-lines and how determining poles in permanent magnets can be very misleading, as are function of the shape and combined effect of many fields. Direction of field lines does not define what or where pole is, it's definitely different for electric and magnetic fields, so do not expect field lines to be the same for magnetic and electric monopoles.

FORCE-LINES matter, not field-lines, ok?

Originally Posted by inow
What you are calling a monopole is not a monopole at all... mostly since it does not act as a source or a sink of either electric nor magnetic field. The field lines neither originate nor end on the object, but instead they form a closed loop.
So? Who did ever define filed-lines have anything to do force-lines? Magnetic force is PERPENDICULAR to magnetic field, so FORCE-LINES actually do point in the direction of the charge, hence two parallel current carrying wires, or electron beams, attract and even contract.

- "The Z-pinch is an application of the Lorentz force, in which a current-carrying conductor in a magnetic field experiences a force. One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, the wires will be pulled toward each other. The Z-pinch uses this effect: the entire plasma can be thought of as many current-carrying wires, all carrying current in the same direction, and they are all pulled toward each other by the Lorentz force, thus the plasma contracts."

Originally Posted by inow
The circular magnetic field lines you show actually have both a magnetic field line entering and leaving each point. Once you see that, you can see clearly that it means what you've shown cannot be a monopole.
According to whom? Who said that? Tornados and whirlpools are "monopole fields" with similar circular field direction, yet the force acts inwards, toward less density. Field-lines and the direction of the FIELD has nothing to do with what pole is, it is not the same as the direction of the FORCE.

How many poles does this hill have?

Again, force lines are perpendicular to field lines.

Originally Posted by inow
AFAICT, you are looking at the field after it's been transformed into a moving frame (the behavior in a moving frame and a rest frame are not the same), and all you really have there is a loop of wire with a current passing through it... aka a dipole.
Dipole? Loop? Wire does not need to form a circular loop, like wire from wall to your TV. For the simplicity you should then imagine single electron in single instant, whatever frame, traveling in a straight line, or electron beam. This field exist in every moment whether is electron moving in straight line or not. So, where exactly are north and south poles if electron is moving as shown on that image, left-right, up-down, front-behind?

The most likely explanation here is that you are defining "monopole" differently than it is defined in the physics community. That's simple enough to correct though, so good luck.
The definition of "pole" is "origin of the field", the point where field is strongest. That's exactly how poles are defined in every single physics equation. Look at it:

Can you give some reference to your definition of what pole and monopole is?

Without knowing where is the origin of magnetic field how do you imagine to sort out coordinates, how do you calculate distance vector "r", where do your vectors start, how do you calculate magnitude if you don't know where are the centers of your magnetic fields?

How many poles do you see in that equation above?

5. Originally Posted by DRUM
Where did you get your definition from?

Monopole means one pole. Dipole means two poles. Ok?
Ah. I see. You're just here to play semantic games. No thanks. I really have no interest in doing that with you. Enjoy.

Except this:

Originally Posted by DRUM
Pole is the place of origin of magnetic field, the place from where its magnitude drops off by 1/r^2 if it is monopole, the point where the field is strongest. Yes?
1/r^2 only applies in a particle's rest frame. You are trying to apply it in a moving frame, which is why you are mistaken.

And, since you keep asking "who said this" and "who said that," I'll go ahead and let you know it was a fellow by the name of Maxwell... James Clerk.

6. Originally Posted by inow
Originally Posted by DRUM
Where did you get your definition from?

Monopole means one pole. Dipole means two poles. Ok?
Ah. I see. You're just here to play semantic games. No thanks. I really have no interest in doing that with you. Enjoy.

Except this:

Originally Posted by DRUM
Pole is the place of origin of magnetic field, the place from where its magnitude drops off by 1/r^2 if it is monopole, the point where the field is strongest. Yes?
1/r^2 only applies in a particle's rest frame. You are trying to apply it in a moving frame, which is why you are mistaken.

And, since you keep asking "who said this" and "who said that," I'll go ahead and let you know it was a fellow by the name of Maxwell... James Clerk.
You are correct.

Drum is out in left field somewhere. Even he probably doesn't know precisely where.

7. @DrRocket,

Your arguments are even more convincing than his. Thanks for that insult there, now I have to challenge you because of that. Make some statement if you can, try to prove me wrong, do you dare to attempt? Do you accept the challenge, mate, what say you?

Originally Posted by inow
Originally Posted by DRUM
Where did you get your definition from?

Monopole means one pole. Dipole means two poles. Ok?
Ah. I see. You're just here to play semantic games. No thanks. I really have no interest in doing that with you. Enjoy.
What in the world is this?!! Are you some kid, or is this some kind of joke!??

"Mono" does mean "one" or "single"; "Di" actually is prefix for "two" or "pair".

Definition of "pole" is "origin of the field", the point where the field is strongest.

That's exactly how poles are defined in every single physics equation. Look at it:

a.) Without knowing where is the origin of magnetic field how do you imagine to sort out coordinates, how do you calculate distance vector "r", how do you calculate magnitude if you don't know where are the centers (poles) of your magnetic fields?

b.) If it is dipole, as you say, then where are the south and north poles?

c.) What in the world do you think "monopole "and "dipole" means and how many poles should they have?

d.) Why the magnitude of this magnetic field diverges towards this only one pole with 1/r^2, just like with gravity and electric monopole fields? Why not 1/r^3 like real dipole magnetic fields?

http://en.wikipedia.org/wiki/Dipole

Originally Posted by inow
1/r^2 only applies in a particle's rest frame. You are trying to apply it in a moving frame, which is why you are mistaken.
That's false. Where did you get that from? This field is called "magnetic field of a MOVING CHARGE". Do you see velocity "v" in that equation above?

Biot-Savart law,
http://en.wikipedia.org/wiki/Biot-savart

The Biot–Savart law is used to compute the magnetic field generated by a steady current, i.e. a continual flow of charges, for example through a wire...

What you think applies, 1/r? What equation do you suggest?

Originally Posted by inow
And, since you keep asking "who said this" and "who said that," I'll go ahead and let you know it was a fellow by the name of Maxwell... James Clerk.
You're mistaken, as I already explained, learn what divergence is.

Can you provide some online reference to what you think Maxwell said?

8. Originally Posted by DRUM
What you think applies, 1/r? What equation do you suggest?

One of your problems is your assumption of a point charge, while trying to describe a wire. The equation I offered also comes from the Biot-Savart Law, and is the more correct form since it takes your equation and integrates it over the length of the wire.

Originally Posted by DRUM
You're mistaken, as I already explained, learn what divergence is.
The divergence of the magnetic field is zero. Ergo, no monopoles.

I refer you now back to the first comment in my previous post.

Originally Posted by inow
I see. You're just here to play semantic games. No thanks. I really have no interest in doing that with you. Enjoy.

9. Originally Posted by inow

I refer you now back to the first comment in my previous post.

You're just here to play semantic games. No thanks. I really have no interest in doing that with you. Enjoy.
I'm not playing with words, I am asking you questions. I gave you explanations and references, equations and definitions, pictures and diagrams.. you think that's some kind of magic trick with words? Fine, you don't have to believe it, you just need to realize what you said is wrong. So, can you please explain yourself?

a.) Where do you see divergence is zero?

http://en.wikipedia.org/wiki/Divergence - "In vector calculus, divergence is an operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar... More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point."

Don't you see magnitude diverges with 1/r^2, directly towards only one place?

b.) How do you use equations without knowing where is the origin of magnetic field, how do you imagine to sort out coordinates, calculate distance, how do you calculate magnitude if you don't know where are the centers (poles) of your magnetic fields?

10. Originally Posted by inow
Originally Posted by DRUM
What you think applies, 1/r? What equation do you suggest?

One of your problems is your assumption of a point charge, while trying to describe a wire. The equation I offered also comes from the Biot-Savart Law, and is the more correct form since it takes your equation and integrates it over the length of the wire.
Wrong. Where did you get that equation? You keep hallucinating without providing any reference, just hideous. There is no such equation, do you understand? I'm not describing wire, but single magnetic field of a moving charge - magnetic monopole.

http://en.wikipedia.org/wiki/Biot-savart

Do you see "1/r^2"? Do you see divergence? Do you see one pole?

11. What I see is a rather unpleasant human being whom I figure must be in seventh or eighth grade who refuses to accept counter examples and ignores the fact that his presentation has been shown flawed. I also see my own lack of desire to continue this nonsense with you. Enjoy.

12. Here you go:
http://en.wikipedia.org/wiki/Magneti....27s_equations

divergence of B = 0

The problem is that you are talking about magnetic force, which has nothing to do with monopoles or dipoles, since this force depends on the presence (and position) of an object to exert the force on.

What you are looking for is the magnetic flux density B.

You should probably read some basic things on electromagnetism. The wikipedia site I linked to could be a place to start.

13. Originally Posted by DRUM
@DrRocket,

Your arguments are even more convincing than his. Thanks for that insult there, now I have to challenge you because of that. Make some statement if you can, try to prove me wrong, do you dare to attempt? Do you accept the challenge, mate, what say you?

Originally Posted by inow
Originally Posted by DRUM
Where did you get your definition from?

Monopole means one pole. Dipole means two poles. Ok?
Ah. I see. You're just here to play semantic games. No thanks. I really have no interest in doing that with you. Enjoy.
What in the world is this?!! Are you some kid, or is this some kind of joke!??

"Mono" does mean "one" or "single"; "Di" actually is prefix for "two" or "pair".

Definition of "pole" is "origin of the field", the point where the field is strongest.

That's exactly how poles are defined in every single physics equation. Look at it:

a.) Without knowing where is the origin of magnetic field how do you imagine to sort out coordinates, how do you calculate distance vector "r", how do you calculate magnitude if you don't know where are the centers (poles) of your magnetic fields?

b.) If it is dipole, as you say, then where are the south and north poles?

c.) What in the world do you think "monopole "and "dipole" means and how many poles should they have?

d.) Why the magnitude of this magnetic field diverges towards this only one pole with 1/r^2, just like with gravity and electric monopole fields? Why not 1/r^3 like real dipole magnetic fields?

http://en.wikipedia.org/wiki/Dipole

Originally Posted by inow
1/r^2 only applies in a particle's rest frame. You are trying to apply it in a moving frame, which is why you are mistaken.
That's false. Where did you get that from? This field is called "magnetic field of a MOVING CHARGE". Do you see velocity "v" in that equation above?

Biot-Savart law,
http://en.wikipedia.org/wiki/Biot-savart

The Biot–Savart law is used to compute the magnetic field generated by a steady current, i.e. a continual flow of charges, for example through a wire...

What you think applies, 1/r? What equation do you suggest?

Originally Posted by inow
And, since you keep asking "who said this" and "who said that," I'll go ahead and let you know it was a fellow by the name of Maxwell... James Clerk.
You're mistaken, as I already explained, learn what divergence is.

Can you provide some online reference to what you think Maxwell said?

Div B = 0 (Gauss's Law, one of the 4 Maxwell Equations)

This says it all.

If you want a reference try any book on classical electrodynamics, Jackson's book will do nicely.

http://en.wikipedia.org/wiki/Maxwell%27s_equations

Now sonny, go learn some electrodynamics. You don't know what in the hell you are talking about.

14. Originally Posted by Bender
Here you go:
http://en.wikipedia.org/wiki/Magneti....27s_equations

divergence of B = 0

The problem is that you are talking about magnetic force, which has nothing to do with monopoles or dipoles, since this force depends on the presence (and position) of an object to exert the force on.
No. Those that define sink and source are actually called FORCE-LINES, not field-lines, it's just that everyone seem to confuse magnetic field-lines with force-lines. Conclusion in that Wikipedia article is either wrong or theoretical postulate. What I'm talking about here you can experimentally confirm. Equations that do describe this situation can tell you exactly where and how many poles there are, how their magnitude changes, while Maxwell equations, nor special relativity, include Lorentz force or have substitute for it, so that's not the place to look for explanation really.

A.) Magnetic field MAGNITUDE converges towards moving charge or not?

http://en.wikipedia.org/wiki/Divergence
- "In vector calculus, divergence is an operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar."

B.) Magnitude is strongest in the center, then drops off with 1/r^2, or not?

C.) How many poles do you say magnetic field of moving charge has?

15. A magnetic monopole is a magnetic field whose magnetic field in the rest frame of the source charge is given by:

where is the unit radial vectorfield, and q is the monopole charge. The above formula is the definition of a magnetic monopole, and as such, it is not open to debate. See for example page 29 of "Some elementary gauge theory concepts" by Chan Hong-Mo and Tsou Sheung Tsun. Or see page 248 of David Griffiths' "Introduction to electrodynamics", Third Edition.

The B-field in your example does not satisfy the above equation, therefore, by definition, it cannot be a magnetic monopole.

16. Originally Posted by DrRocket
Div B = 0 (Gauss's Law, one of the 4 Maxwell Equations)

This says it all.

If you want a reference try any book on classical electrodynamics, Jackson's book will do nicely.

http://en.wikipedia.org/wiki/Maxwell%27s_equations

Now sonny, go learn some electrodynamics. You don't know what in the hell you are talking about.
No, my dear, you're just blindly repeating what you don't understand.

A.) Magnetic field MAGNITUDE converges towards moving charge or not?

B.) Maxwell equations do not include 'magnetic fields if moving charge', ok?

C.) How many poles, do you say kiddo, magnetic field of moving charge has?

17. Originally Posted by salsaonline
A magnetic monopole is a magnetic field whose magnetic field in the rest frame of the source charge is given by:

where is the unit radial vectorfield, and q is the monopole charge. The above formula is the definition of a magnetic monopole, and as such, it is not open to debate. See for example page 29 of "Some elementary gauge theory concepts" by Chan Hong-Mo and Tsou Sheung Tsun. Or see page 248 of David Griffiths' "Introduction to electrodynamics", Third Edition.

The B-field in your example does not satisfy the above equation, therefore, by definition, it cannot be a magnetic monopole.
A.) Can you give some online reference for that, like Wikipedia?

B.) The B-field of a moving charge actually satisfies that equation.

C.) How many poles, you say, magnetic field of a moving charge has?

18. Originally Posted by DRUM
Originally Posted by DrRocket
Div B = 0 (Gauss's Law, one of the 4 Maxwell Equations)

This says it all.

If you want a reference try any book on classical electrodynamics, Jackson's book will do nicely.

http://en.wikipedia.org/wiki/Maxwell%27s_equations

Now sonny, go learn some electrodynamics. You don't know what in the hell you are talking about.
No, my dear, you're just blindly repeating what you don't understand.

A.) Magnetic field MAGNITUDE converges towards moving charge or not?

B.) Maxwell equations do not include 'magnetic fields if moving charge', ok?

C.) How many poles, do you say kiddo, magnetic field of moving charge has?
Sonny I have understood electrodynamnics longer than you have been alive.

Your questions are nonsensical. They do nothing more than demonstrate a complete and total lack of understanding of Maxwell'e equations and classical electrodynamics.

A magnitude is a scalar and cannot converge toward anything. That question makes no sense and simply demonstrates that you no idea of the difference between a vector field and a scalar field. In fact "converges towards anything" doesn't really make sense for vector fields although it is pictorially similar to the notion of the divergence of a field near a source. The content of div B = 0 is that there are no sources for the magnetic field. So your question A is nonsensical. Go learn something about vector analysis and Maxwell's equations.

Maxwell's equations embody ALL of classical elelctrodynamics including the magnetic field of a a moving charge. In fact, in classical electrodynamics a moving charge is the ONLY way to obtain a magnetic field. Quantum mechanically there are intrinsic magnetic moments of particles, but that came a bit after Maxwell and is not a classical effect. The answer to your question B is a resounding NO, not "OK", and you again have no idea what you are talking about.

A moving charge creates a magnetic field following Ampere's law, which in the face of a static E field takes the form

curl B = mu J

That does not have pole in the sense of a permanent magnet and again your question makes no sense and simply demonstrates another deep level of ignorance of electrodynamics.

So, kiddo you have now rather totally embarrassed yourself, assuming you have sufficient perception to be embarrassed.

Go read a good book on electrodynamics. If Jackson is beyond your mathematical capabilities perhaps Marions' Classical Electrolmagnetic Radiation would meet your needs. If you cannot read and understand that book, I understand that there openings for shepherds and you might consider a different career.

The equation div B = 0, one of Maxwell's equations is nothing more and nothing less than the statement that magnetic monopoles do not exist.

If you are looking for magnetic monopoles you are going to have get fairly exotic and start delving into speculative particle physics. You absolutely are not goint to get there through Maxwell's equations. They utterly forbid monopoles.

Now go learn some physics. It is clear from your posts that you have a mountain of material to learn before you can be taken seriously.

19. Originally Posted by DrRocket
Sonny I have understood electrodynamnics longer than you have been alive.

Your questions are nonsensical. They do nothing more than demonstrate a complete and total lack of understanding of Maxwell'e equations and classical electrodynamics.

A magnitude is a scalar and cannot converge toward anything. That question makes no sense and simply demonstrates that you no idea of the difference between a vector field and a scalar field. In fact "converges towards anything" doesn't really make sense for vector fields although it is pictorially similar to the notion of the divergence of a field near a source.
Kiddo, why so angry?

A.) http://en.wikipedia.org/wiki/Convergence - "Convergence is the approach toward a definite value, a definite point, a common view or opinion, or toward a fixed or equilibrium state. In mathematics, it describes limits..."

Convergence meant there is only one point, one limit, where magnitude is approaching maximum, in this case with 1/r^2, which represents the origin or POLE of this field, just as with gravity and electric monopoles, do you understand now?

B.) http://en.wikipedia.org/wiki/Divergence - "In vector calculus, divergence is an operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar."

Do you accept this definition?

C.)

Is this equation that describes magnetic field of a moving charge?

The content of div B = 0 is that there are no sources for the magnetic field. So your question A is nonsensical. Go learn something about vector analysis and Maxwell's equations.
Ughh... don't blame me for your inability to understand. Did you just say there is no source for the magnetic field? Then, what is the source of magnetic field of a moving charge, if not moving charge?

Maxwell's equations embody ALL of classical elelctrodynamics including the magnetic field of a a moving charge. In fact, in classical electrodynamics a moving charge is the ONLY way to obtain a magnetic field. Quantum mechanically there are intrinsic magnetic moments of particles, but that came a bit after Maxwell and is not a classical effect. The answer to your question B is a resounding NO, not "OK", and you again have no idea what you are talking about.

A moving charge creates a magnetic field following Ampere's law, which in the face of a static E field takes the form

curl B = mu J

That does not have pole in the sense of a permanent magnet and again your question makes no sense and simply demonstrates another deep level of ignorance of electrodynamics.
Did you just say - moving charge creates a magnetic field with NO poles?

Are you making fun of yourself? Anyhow, look:
http://en.wikipedia.org/wiki/Maxwell_equations

As I told you, Maxwell equations do not include Lorentz force, do you see?

That does not have pole in the sense of a permanent magnet...
Not a dipole like permanent magnet? It's a NOPOLE, eh?

Why is not the place where this field originates and is strongest a pole?

20. Originally Posted by DrRocket
If you are looking for magnetic monopoles you are going to have get fairly exotic and start delving into speculative particle physics.
http://en.wikipedia.org/wiki/Magnetic_monopoles

- "Dirac showed that the existence of magnetic monopoles was consistent with Maxwell's equations only if electric charges are quantized, which is observed."

Maxwell's equations - "The standard form of the equations provides for an electric charge, but posits no magnetic charge. Except for this, the equations are symmetric under interchange of electric and magnetic fields... Fully symmetric equations can also be written if one allows for the possibility of "magnetic charges" analogous to electric charges."

You're confusing theoretical assumptions with experimental facts and plain logic.

You absolutely are not goint to get there through Maxwell's equations. They utterly forbid monopoles.
Someone's prejudice and hallucinations are forbidding us reality, eh? Maxwell equations do not include Lorentz force, and I said already that's not a good place to look for this answer. I'm not trying to use them for anything, you and other people brought them up here.

21. Drum, I think you should take a course in classical electrodynamics before you spend too much time on this.

22. Folks it is time to move this discussion out of physics and into Pseudoscience or some suitable forum.

This is certainly not physics.

23. Originally Posted by salsaonline
Drum, I think you should take a course in classical electrodynamics before you spend too much time on this.
Salsa, I have 7 years of university education, physics and computer science, plus 17 years of laboratory practice in experimental physics and manufacturing. So, what part do you not understand?

CAN YOU RESPOND TO THIS PLEASE:

A.) How many poles, you say, magnetic field of a moving charge has?

B.) The B-field of a moving charge actually satisfies that equation, yes?

24. Originally Posted by DrRocket
Folks it is time to move this discussion out of physics and into Pseudoscience or some suitable forum.

This is certainly not physics.
What? Can you not even articulate?

All those definitions, imagines and equations are from Wikipedia.

25. Originally Posted by DRUM
I have 7 years of university education, physics and computer science, plus 17 years of laboratory practice in experimental physics and manufacturing.
Sorry, but it really doesnt seem like it.

Originally Posted by DRUM
CAN YOU RESPOND TO THIS PLEASE:

A.) How many poles, you say, magnetic field of a moving charge has?
A pole is simply defined as a point where the magnetic field is "entering" or "exiting". For example, imagine the earth is a particle. It still has a north and a south pole, even though it is only a single particle. A particle is not a pole. A single particle still always has 2 poles.

Originally Posted by DRUM
B.) The B-field of a moving charge actually satisfies that equation, yes?
Whether it does or it doesnt has nothing to do with whether it is a monopole or not, which it isnt.

26. Originally Posted by Waveman28
A pole is simply defined as a point where the magnetic field is "entering" or "exiting".
No. Can you provide some reference to that definition?

Pole is the origin/cause of the field, the place where the field is strongest, the place towards which the opposite pole will be attracted and from which the like pole will be repelled. In case of monopoles, the point from which the filed magnitude drops off with inverse-square law.

http://en.wikipedia.org/wiki/Biot-savart

Vorticity and solitons, whirlpools and tornadoes have circular fields with perpendicular/radial attraction/repulsion. -- Look at the place where the wing-tip just passed, this is very much like magnetic field of a moving charge. Tip of the wing is where the pole is, the cause. Magnetic field lines are circular, yet the force is perpendicular, radial. You should not now be surprised to hear that Biot-Savart law is used in fluid dynamics and aerodynamic just as well as in magnetism.

For example, imagine the earth is a particle. It still has a north and a south pole, even though it is only a single particle. A particle is not a pole. A single particle still always has 2 poles.
That is magnetic field due to spin.

Actually, a single electron will have 5 poles.

1 Electric monopole
1 Gravity monopole
1 Magnetic monopole due to spatial motion
2 Magnetic fields, one magnetic dipole due to spin

Anyhow, we are talking about 3.) 'magnetic field of a moving charge', something like this:

Where are these two poles of yours, where are the north and south poles?

Do you see the coordinate of the center of this magnetic field are the same of as that of electric field, and do you see that field magnitude drops off with 1/r^2?

27. With the formula you've given us, go ahead and compute the flux of the B-field across a closed cylinder containing the particle, whose axis lies along the path of the particle. You'll find quite easily that the flux is zero. So, while the formula you've given us definitely looks similar to the formula for the E-field of a stationary charge, it is not the same thing.

Bottom line: point charges give rise to fields with non-zero flux across surfaces that contain them. That's pretty much the definition of what a point charge is. In your situation, the moving charge IS a point charge for the E-field, but NOT for the B-field.

28. Originally Posted by salsaonline
Bottom line: point charges give rise to fields with non-zero flux across surfaces that contain them. That's pretty much the definition of what a point charge is.
Yes, the magnetic flux is non-zero, so you actually agree about magnetic monopoles then?

"across surfaces that contain them", that's not correct way to say it. Magnetic flux is defined as through an element of area perpendicular to the direction of magnetic field. Flux is always in the direction of the force. Do not assume anything contains anything, do not assume "closed surfaces". We know about fields only indirectly by observing the force. Field-lines do not need to be in the same direction as force lines. Force makes things move and does the work, not fields. Forget the direction of the field-lines already, that has nothing to do with the number of poles.

With the formula you've given us, go ahead and compute the flux of the B-field across a closed cylinder containing the particle, whose axis lies along the path of the particle.
Yes, and flux is non-zero in the radial/perpendicular direction, just as it should be. Are you refuting yourself, or are you on my side now, all of a sudden?

You'll find quite easily that the flux is zero.
Wrong.

http://en.wikipedia.org/wiki/Magnetic_flux
- "Magnetic flux is a measure of quantity of magnetism, taking into account the strength and the extent of a magnetic field... The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element."

So, while the formula you've given us definitely looks similar to the formula for the E-field of a stationary charge, it is not the same thing.
So, you know now what flux is, but do you understand what is that all about? What and why flux and divergence have anything to do with the number of poles and what pole actually is? Those are all mathematical concepts of very simple, everyday things and there is no need to complicate matter. All we are trying to figure out is how many points of attraction/repulsion there are in a given area.

http://en.wikipedia.org/wiki/Divergence
- "In physical terms, the divergence of a three dimensional vector field is the extent to which the vector field flow behaves like a source or a sink at a given point. If the divergence is nonzero at some point then there must be a source or sink at that position. Note that we are imagining the vector field to be like the velocity vector field of a fluid (in motion) when we use the terms flow, sink and so on."

Tornadoes and whirlpools, they are monopole fields, only one sink, yes? So, do we really need to talk about flux, divergence, Maxwell's or Gauss's assumptions, if we only need to count these sinks? You can do it at home, with battery, wire and permanent magnet.

Magnetic field of a moving charge is a sink and source obviously, just like electric monopoles are, hence two parallel current carrying wires can attract and repel due to these fields, depending on direction of the field-lines, which will determine the direction of the force.

In your situation, the moving charge IS a point charge for the E-field, but NOT for the B-field.
Then, how many points B-field has, and where they are? You never actually used any of those equations, have you? My job is to simulate interaction of these particles and visualize magnetic and electric fields, so based on this experience I would suggest to you, and to some other people I spoke with here even more, to stop pretending that you know, that way you will never learn.

29. If you want to convince me, calculate the flux of the B field over the cylindrical surface I indicated and demonstrate that it is non-zero. Don't just say "wrong"--I'm a mathematician, and my expertise is in differential topology, so I'm not likely to make a mistake in calculating the flux of a vectorfield. If you think I'm mistaken, the only thing that will change my mind is a clear calculation to the contrary.

30. Originally Posted by salsaonline
If you want to convince me, calculate the flux of the B field over the cylindrical surface I indicated and demonstrate that it is non-zero. Don't just say "wrong"
I did not just say "wrong", I also gave you...

1.) definitions...

http://en.wikipedia.org/wiki/Magnetic_flux
- "Magnetic flux is a measure of quantity of magnetism, taking into account the strength and the extent of a magnetic field... The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element."

http://en.wikipedia.org/wiki/Divergence
- "In physical terms, the divergence of a three dimensional vector field is the extent to which the vector field flow behaves like a source or a sink at a given point. If the divergence is nonzero at some point then there must be a source or sink at that position. Note that we are imagining the vector field to be like the velocity vector field of a fluid (in motion) when we use the terms flow, sink and so on."

2.) and illustrations...

3.) and equations...

http://en.wikipedia.org/wiki/Biot-savart
http://en.wikipedia.org/wiki/Lorentz_force

5.) and more explanation...

http://en.wikipedia.org/wiki/Z-pinch
- "The Z-pinch is an application of the Lorentz force, in which a current-carrying conductor in a magnetic field experiences a force. One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, the wires will be pulled toward each other. The Z-pinch uses this effect: the entire plasma can be thought of as many current-carrying wires, all carrying current in the same direction, and they are all pulled toward each other by the Lorentz force, thus the plasma contracts."

We are counting number of poles, the points of attraction/repulsion.
Yet, everyone keeps talking about the stupid direction of the field-lines?!

I'm a mathematician, and my expertise is in differential topology, so I'm not likely to make a mistake in calculating the flux of a vectorfield. If you think I'm mistaken, the only thing that will change my mind is a clear calculation to the contrary.
I gave you equations, ok?

So, what else do you need, mathematician guy? To chew it for you?

Shall I make a computer simulation, animation? What more do you want?

You say you're an expert with math, so show us. How do you get flux is zero?

You wouldn't just trust my math when you can do it better in a few seconds, right?

Just as is obvious from Newton's law of universal gravitation:

...that gravity pole is located on those X,Y,Z coordinates of mass "m", and so as is obvious electric pole is located on those X,Y,Z coordinates of charge "q" from Coulomb's law:

...so, it's just as obvious magnetic pole is located on those X,Y,Z coordinates of charge "q" from Biot-Savart law:

Stop confusing yourself with the flux, it's only an imaginary context, attempt to illustrate fields without the fluid, without Aether. We are talking about the number of poles, so just count the bloody poles, for the love of drugs, will you?! None, one, two, many?

31. I completely understand the analogy you're suggesting. But notice that because we're taking the cross product v x r the field lines are always parallel to the surface of a cylinder whose axis is centered along the direction of motion. It follows that the flux of B across a closed cylinder containing the particle, with axis centered along the direction of motion, is zero.

Moreover, since div(B) is zero away from the locus of the particle, the above observation, combined with the divergence theorem, implies that the flux of B across ANY surface containing the particle is zero.

I agree that the B-field you've written down has a single pole at the locus of the particle. But that's not what people mean by the term "monopole" in physics. A monopole, by definition, must give rise to a non-zero flux across some surface. If you don't like that definition, that's a whole different story. I didn't invent the term.

If creating a magnetic monopole were as easy as moving an electron at a constant velocity, don't you think the physics community would have noticed this somewhere in the last 100 years? That the existence/non-existence of magnetic monopoles remains an elusive and speculative topic in physics should give you pause.

32. Originally Posted by salsaonline
But notice that because we're taking the cross product v x r the field lines are always parallel to the surface of a cylinder whose axis is centered along the direction of motion.
You are talking about the direction of the field lines again, that's not the direction of the flux. Please notice there is yet another cross product in magnetic force equation, that's the direction of the flux. Flux is perpendicular to the field lines, i.e. Lorenz force is perpendicular to B-field, ok?

It follows that the flux of B across a closed cylinder containing the particle, with axis centered along the direction of motion, is zero.
It follows from what exactly? Some experiment?
Assumption? What equation are you talking about?

Moreover, since div(B) is zero away from the locus of the particle, the above observation, combined with the divergence theorem, implies that the flux of B across ANY surface containing the particle is zero.
No, what equations do you use, special relativity, Maxwell, what?

Magnetic flux through an open surface
http://en.wikipedia.org/wiki/Magnetic_flux
-"While the magnetic flux through a closed surface is always zero, the magnetic flux through an open surface is an important quantity in electromagnetism... The EMF is determined in this equation in two ways: first, as the work per unit charge done against the Lorentz force..."

Start of this false, but it proves the point just enough.

A monopole, by definition, must give rise to a non-zero flux across some surface. If you don't like that definition, that's a whole different story. I didn't invent the term.
Flux is non-zero. Where do you see flux is zero?

What equations or experiments are you looking at?

If creating a magnetic monopole were as easy as moving an electron at a constant velocity, don't you think the physics community would have noticed this somewhere in the last 100 years? That the existence/non-existence of magnetic monopoles remains an elusive and speculative topic in physics should give you pause.
Do not underestimate the power of human stupidity.

33. I should have said the flux of B across any CLOSED surface containing the particle is zero. I'm used to using the word "surface" to mean "closed surface".

All I'm using is (1) the definition of a magnetic monopole according to the physics community and (2) basic vector calculus. I've provided two references for (1). For (2), consult any book on advanced calculus or any good book on electrodynamics.

Wikipedia, while often useful, is not always a reliable reference with regard to technical topics. While I'm not claiming Wikipedia to be exactly "wrong" on any particular point, their explanations can be misleading to those who are not already familiar with the subject. This is true of any encyclopedia that is written for a wide audience.

I encourage you to consult a genuine reference on electrodynamics. David Griffiths' book "Introduction to Electrodynamics" would be a great place to start.

At bottom, you are simply misunderstanding the DEFINITION of a technical term, namely "magnetic monopole". Having a field (whether a force field or B-field) with a single singularity at the locus of a particle is NOT sufficient to call something a "monopole".

34. Have you noticed you are not responding to my questions? You will never understand your confusion if you don't at least try to provide some reference to support your statements, actually look at what you are misinterpreting, you know?

Originally Posted by salsaonline
All I'm using is (1) the definition of a magnetic monopole according to the physics community and (2) basic vector calculus. I've provided two references for (1). For (2), consult any book on advanced calculus or any good book on electrodynamics.
What calculus? What equations?
Can you write it here so we can see?

Where do you see flux is zero? Show us!

I should have said the flux of B across any CLOSED surface containing the particle is zero.

Magnetic flux through a closed surface
http://en.wikipedia.org/wiki/Magnetic_flux
- "Gauss's law for magnetism, which is one of the four Maxwell's equations, states that the total magnetic flux through a closed surface is equal to zero. (A "closed surface" is a surface without boundaries, such as the surface of a sphere or a cube, but not like the surface of a disk.) This law is a consequence of the empirical observation that magnetic monopoles have never been found."

A.) Do you really mean to say cylinder is CLOSED surface?

B.) Do you realize Maxwell equations don't contain Lorentz force?

C.) 'No monopoles' is only ASSUMPTION based on lack of "evidence"?

You can not make definition based on your blindness, that's assumption, and it is not "across", as I already demonstrated, but 'through'. You are using wrong equations obviously, magnetic flux of magnetic field of a moving charge is determined with Lorentz force, do you understand? Do you not agree? What equations are you using to calculate flux and divergence?

Wikipedia, while often useful, is not always a reliable reference with regard to technical topics. While I'm not claiming Wikipedia to be exactly "wrong" on any particular point, their explanations can be misleading to those who are not already familiar with the subject. This is true of any encyclopedia that is written for a wide audience.

I encourage you to consult a genuine reference on electrodynamics. David Griffiths' book "Introduction to Electrodynamics" would be a great place to start.

At bottom, you are simply misunderstanding the DEFINITION of a technical term, namely "magnetic monopole". Having a field (whether a force field or B-field) with a single singularity at the locus of a particle is NOT sufficient to call something a "monopole".
Fascinating. You keep presenting your misinterpretation, your OPINION without any actual reference or support to your statements. Why is it so hard to Google the Internet and provide at least one link that confirms what you say?

Perhaps there is no confirmation for what you're talking about on the whole Internet, maybe Wikipedia is not aware of your definitions and equations, so go ahead and take a citation from whatever book you think confirms your statements, quote the book, can you do that?

35. First of all, I've given you two references, with the actual page numbers. It would be a simple matter for you to look for these books in a university library. Or, you might even be able to look them up on google books. Don't expect me to do all your research for you--this is your project, not mine.

As for writing out calculations, I've described in words exactly what sort of calculation you could do, and outlined why the calculation will come out to zero.

By "closed cylinder", I of course mean a cylinder that has been capped off at both ends. This is a closed surface homeomorphic to a sphere.

Here is a quote from the gauge theory book I cited in an earlier post:

"Our contention above was that the case of Figure 2.4b should correspond to a monopole, in this case a magnetic charge. Let us see now whether such a claim can be maintained. We recall that 'charge' in electromagnetism is conventionally defined as a source of flux; thus, in the case of magnetic charge, one of magnetic flux. To show that there is a source of magnetic charge inside the surface , we shall need to measure the total magnetic flux emerging from that surface."

--"Some elementary gauge theory concepts", Chan Hong-Mo, Tsou Sheung Tsun, page 19-20.

Also, later on page 20:

"...the definition above of a magnetic monopole as a topological obstruction is equivalent to its conventional definition as a source of magnetic flux."

36. As for writing out calculations, I've described in words exactly what sort of calculation you could do, and outlined why the calculation will come out to zero.
What equations did you use? Can you write it down, please?

http://en.wikipedia.org/wiki/Lorentz_force
Can you understand Lorentz force (flux) is perpendicular to B-field?

"Our contention above was that the case of Figure 2.4b should correspond to a monopole, in this case a magnetic charge. Let us see now whether such a claim can be maintained. We recall that 'charge' in electromagnetism is conventionally defined as a source of flux; thus, in the case of magnetic charge, one of magnetic flux. To show that there is a source of magnetic charge inside the surface \Sigma, we shall need to measure the total magnetic flux emerging from that surface."
Yes, that's the DEFINITION we are talking about for a while. Now, all you need to do is to write down your equations for magnetic flux of moving charge. What equation do you use to calculate this flux?

"...the definition above of a magnetic monopole as a topological obstruction is equivalent to its conventional definition as a source of magnetic flux."
What equation did you use to calculate flux of magnetic field of moving charge?

Flux of magnetic field of a moving charge is NON-ZERO, otherwise two parallel current carrying wires would not interact, there would be no Lorentz force and no Z-pinch. Saying the flux is zero means there is no attraction/repulsion at all, do you understand?

37. There's no flux across a CLOSED SURFACE. Obviously there's a flux over a surface with boundary.

38. Originally Posted by salsaonline
There's no flux across a CLOSED SURFACE. Obviously there's a flux over a surface with boundary.
It's already obvious you assume SOME flux "across" SOME closed surface, even if true, has anything to do with THE flux of magnetic field of a moving charge. Look at the definitions you gave:

-"To show that there is a source of magnetic charge inside the surface, we shall need to measure the total magnetic flux emerging from that surface.

...the definition above of a magnetic monopole as a topological obstruction is equivalent to its conventional definition as a source of magnetic flux."

What equation do you use to calculate flux of magnetic field of moving charge?

What experiment do you think measures zero magnetic flux of moving charge(s)?

39. Take the B-field you've written down:

(Up to a constant that's what you've given for B.) We fix a moment in time and choose our coordinates so that the particle is at the origin. One thing that's immediate from the above formula is the following: If you choose your coordinate system so that points in the z-direction, and if you use cylindrical coordinates where s denotes distance from the z-axis, and denotes angle of rotation about the z-axis, then B is of the form

where is the unit vectorfield that points in the angular direction, and theta is the angle the position vector makes with the z-axis. Notice that B is defined everywhere except at the origin, since B vanishes along the z-axis away from the origin.

Now consider a closed cylinder with axis along the z-axis, capped off at z = a and z = -a (so that the cylinder contains the particle in its interior). We wish to compute:

where dA is the area form on the closed cylinder, and is the unit vector normal to the surface of the cylinder.

There are three parts to this integral: the two tops of the cylinder and the side of the cylinder. First the side:

Along the side of the cylinder, . Since B is proportional to , . So the flux along the side of the cylinder is zero.

Finally the two caps: The normal vector on the top and bottom of the cylinder is . Since this is also perpendicular to , the integral of along the two caps is also identically zero.

It follows that the total flux of B across this cylinder is zero. Notice that the radius and height of the cylinder did not matter in the above computation.

Finally, let S be ANY closed surface containing the origin. We'll show the flux of B across S is zero. To do this, first choose a cylinder C containing the origin which is sufficiently small so that C is contained in S. Then B is defined everywhere in the region bounded by S and C. One easily computes that the divergence

in this region. By the divergence theorem, the integral of the divergence of B over this region is the difference between the flux of B across S and the flux of B across C. Since the flux of B across C = 0, we have that the flux of B across S equals 0 as well.

This shows that the flux of B across any closed surface containing the charge is zero. Hence, B is not a monopole.

40. Originally Posted by salsaonline
Now consider a closed cylinder with axis along the z-axis, capped off...
CLOSED cylinder?! Why?

That is false assumption without any reference again.

We are talking about magnetic flux of MOVING CHARGES.

Why two parallel current carrying wires attract/repel? Why, if there is no magnetic flux, no magnetic sink or source? So, you equations are inadequate, you are missing one more cross product, you are oblivious to Lorentz force.

Dipole has two sets of field lines that go in in two opposite directions.
Monopole has only one set of field lines and they all go in the same direction.

How many poles do you say magnetic field of moving charge has, none, one, two, many?

With what experiment do you think measures magnetic flux of moving charge is zero if Ampere's force law, Lorentz force experiments like Bubble chambers and Z-pinch experiments all clearly demonstrate attraction/repulsion i.e. sink/source aka POLES?

41. I'm not oblivious to the Lorentz force law. It just doesn't happen to be relevant in this case. But I'm done arguing with you.

I encourage you to actually look up the definition of a magnetic monopole in any respectable physics or math book. If you are unwilling to extend even that much effort, then you should not expect other people to extend the effort to listen to you.

42. Originally Posted by salsaonline
I'm not oblivious to the Lorentz force law. It just doesn't happen to be relevant in this case. But I'm done arguing with you.
Ok. Tuck your tail and run then. Good bye.

Originally Posted by salsaonline
I encourage you to actually look up the definition of a magnetic monopole in any respectable physics or math book. If you are unwilling to extend even that much effort, then you should not expect other people to extend the effort to listen to you.
You encourage me? Why in the world did you not just write it down?! Hahahaa!!

I encourage you to read "The Emperor's New Clothes" by Hans Christian Andersen.

43. Originally Posted by DRUM
Originally Posted by salsaonline
I'm not oblivious to the Lorentz force law. It just doesn't happen to be relevant in this case. But I'm done arguing with you.
Ok. Tuck your tail and run then. Good bye.
You have just given up a sterling opportunity to learn some physics and some mathematics. That is extremely foolish, And predictable.

salsalonline in a very competent mathematician who works on questions suggested by physics, and therefore also quite competent in physics.
Everything that he has told you is correct. Everything. You can either learn something or choose to ignore correct information that is given you. Apparently you have chosen the second option.

You are simply wrong. Not even close. Maxwell's equations are completely consistent with the Lorentz force equation. And one of Maxwell's equations is div B=0. That is nothing more and nothing less than the statement that there is no magnetic "charge", no monopole, in classical electrodynamics.

No hallucination or delusion on your part is going to change that. div B - 0.

This has been explained to you in at least two forums by a least 3 PhD physicists and at least two PhD mathematicians, with no visible effect. You are quite hopeless.

44. Originally Posted by DrRocket
You are simply wrong. Not even close. Maxwell's equations are completely consistent with the Lorentz force equation.
I said Lorentz force is not described with any of the Maxwell equations.

And one of Maxwell's equations is div B=0. That is nothing more and nothing less than the statement that there is no magnetic "charge", no monopole, in classical electrodynamics.
Look at the equation! Where is the explanation?
Try to understand why and how that law came to be.

http://en.wikipedia.org/wiki/Gauss%2..._for_magnetism
- "In physics, Gauss's law for magnetism is one of Maxwell's equations, the four equations that underlie classical electrodynamics. It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not exist. Of course, if monopoles were ever found, the law would have to be modified, as elaborated below."

Can you not see that "law" is just an assumption (based on wrong conclusion)?

Long time ago, someplace important:
- Has anyone seen any magnetic monopoles?

- Everyone: "No."

- Ok, then we have a new law - "there are no magnetic monopoles and magnetic flux through closed surface is zero". We will call this Gauss's law for magnetism and it will be one of Maxwell's equations.

...later, someone finds a monopole:

- Hey, I found a magnetic monopole!

- Everyone: "No, you did not - magnetic monopoles do not exist, no one will ever find them, they are FORBIDDEN by Maxwell's equations!"

- Ay, caramba!

Is this equation for divergence?

http://en.wikipedia.org/wiki/Divergence

45. Originally Posted by DRUM
Originally Posted by DrRocket
You are simply wrong. Not even close. Maxwell's equations are completely consistent with the Lorentz force equation.
I said Lorentz force is not described with any of the Maxwell equations.

Completely irrelevant.

Maxwell's equations completely describe the electromagnetic field. The Lorentz force equation, which is compatible with Maxwell's equations simply describes the force exerted on a test particle by the electric and magnetic components of the field. You cannot use the Lorentz force equation to contradict Maxwelll's equations.

div B = 0

says it all. It is quite simply the statement that there are no monopoles.

Your ignorance of physics in general and classical electromagnetism in particular is profound. You need to go learn some physics. Several references have been provided to you. Go read at least one.

You have no idea what you are talking about. This has been explaine to you by no less than 3 PhD physicists and 2 PhD mathematicians, in complete and rigorous detail. The simple fact that you cannot understand the explanation only serves to accentuate your need to learn basic physics. Hopefully you will not do damage to any newbies naive enough to take you seriously.

div B = 0

46. Originally Posted by DrRocket
div B = 0

says it all. It is quite simply the statement that there are no monopoles.
Hahahaaa. You don't even need to calculate anything, eh? That must be the best equation in the whole physics, it solved itself in advance. That's like proving God with the Bible. You are dogmatic and brainwashed, my friend. That statement says field lines are circular, that's all, nothing else it says. Magnetic force is perpendicular to those circular field-lines.

Have you ever taken some IQ test?

You can not see the left has two of what right has one?

What is the divergence of magnetic dipole, zero as well?

47. There's two big points that you're missing here:

(1) When I demonstrated that the flux of the B-field you wrote down is zero across a closed surface, at no point did I make any reference to Maxwell's equations. I never explicitly assumed anything other than the equation you gave me (plus basic vector calculus). So whether Maxwell's equations need to be modified or not is completely irrelevant to the explanation I gave.

(2) The equation you gave for the B-field can be derived from Maxwell's equations. Since Maxwell's equations already assume no magnetic monopoles, any equation that you derive from Maxwell's equations must, by logical necessity, be consistent with the non-existence of magnetic monopoles.

48. Originally Posted by salsaonline
(2) The equation you gave for the B-field can be derived from Maxwell's equations. Since Maxwell's equations already assume no magnetic monopoles, any equation that you derive from Maxwell's equations must, by logical necessity, be consistent with the non-existence of magnetic monopoles.
Div B = 0

You call that an equation? Built-in result?!
To save you the trouble of thinking?

Yes, it assumes, so logically Maxwell equations are consistent with Maxwell equations and so, as assumption, this particular equation can not prove or disprove anything.

There is nothing to be derived there, you MEASURE and CALCULATE it, NOT ASSUME it. "Div" is divergence, "B" is field, give me the FULL definition/equation and experimental measurements, not this silly equation that already has a result (assumption) with it.

A.) Is divergence of magnetic dipole zero as well?

B.) How many poles you think this field has, none, one, two, many?

C.) How do you define "POLE of a field"? Is that a same thing as sink/source?

49. A monopole is a 2-form on R^3-pt which is closed but not exact. This necessarily implies that the 2-form will "blow up" at the removed point, but that alone isn't sufficient to guarantee that the given form represents some non-trivial cohomology.

50. Originally Posted by salsaonline
A monopole is a 2-form on R^3-pt which is closed but not exact. This necessarily implies that the 2-form will "blow up" at the removed point, but that alone isn't sufficient to guarantee that the given form represents some non-trivial cohomology.
You are not responding to questions:

A.) Is divergence of magnetic dipole zero as well?

B.) How many poles you think this field has, none, one, two, many?

C.) How do you define "POLE of a field"? Is that the same thing as sink/source?

51. Originally Posted by DRUM

You can not see the left has two of what right has one?

What is the divergence of magnetic dipole, zero as well?
Wait... How exactly is the one on the right a monopole? It looks very much like a dipole to me

52. Originally Posted by Arcane_Mathematician
Wait... How exactly is the one on the right a monopole? It looks very much like a dipole to me
Two sets of circles going in opposite direction is very much different from one set of circles all going in the same direction. Perhaps, this is a matter of taste?!!

POLE of a field = extreme, origin, limit, source/sink

Di = two, pair --> DIPOLE = two origins, two source/sinks
Mono = one, single --> MONOPOLE = one origin, one source/sink

Polarity is relative concept. It is defined by the direction of the field-lines. There is no such thing as absolute North and South poles, there is only "same direction" and "opposite direction". -- Magnetic dipole has two sets of circular field lines going in two opposite directions, indicating dual polarity. Therefore, logically, magnetic monopole will have only one set of field lines all going in the same direction, indicating single polarity.

53. Once again, that's not the definition of a magnetic monopole.

54. Originally Posted by salsaonline
Once again, that's not the definition of a magnetic monopole.
What do you think you're doing? Who are you trying to brainwash with that brilliant explanation and convincing arguments? That was general definition for POLE, not magnetic, not monopole, but just 'pole of a field'. It works for gravity fields, electric fields and magnetic dipole fields, ok? -- How did you come up with your conclusion if you can not articulate what do you think 'pole' is and where are they located?

You are not responding to questions:

A.) Is divergence of magnetic dipole zero as well?

B.) How many poles you think this field has, none, one, two, many?

C.) How do you define "POLE of a field"? Is that the same thing as sink/source?

55. no, drum, he's right. IIRC a magnetic monopole would have only one magnetic charge. It would be either wholly positive or wholly negative, and what you are showing is both positive and negative, and thusly a dipole.

the picture at the right has both a source and a sink, btw.

56. Originally Posted by Arcane_Mathematician
a magnetic monopole would have only one magnetic charge.
It does have only one magnetic charge. Magnitude of this magnetic charge drops off with 1/r^2 from the source of this field, its pole - charge "q". Just as it is the case with electric monopole field and electric charge.

Dipoles have two fields - two poles. There is only one field here - one pole. There is only one set of circular field lines here, going in the same direction, indicating single polarity. Magnetic dipole has two sets of circular field lines going in two opposite directions, indicating dual polarity. Why are you ignoring this?

It would be either wholly positive or wholly negative, and what you are showing is both positive and negative, and thusly a dipole.
There is no such thing as absolute magnetic polarity, there is no positive and negative. It's about orientation and direction, there is only attraction and repulsion. Electron, electric monopole, can also do both, attract and repel, just like this magnetic monopole, it can be both sink and source, ok? That does not tell you how many poles, how many fields are there. Pole is a point of attraction/repulsion, simple as that.

So, you saying there there are two opposite magnetic fields there?
Why they do not neutralize each other?

the picture at the right has both a source and a sink, btw.
Not "has", but "can be". Monopoles can 'act' as both.

So, yes, just like electric monopoles, it can be both sink and source.

Now, after you have defined "POLE", let us know how many of those it has, ok?

57. Just as I commented way back on page one... nothing but semantic games.

58. DRUM: I saw you were suspended on Baut ATM, because you "didn't answer questions". It seems to be a common theme. But I'm afraid there are no magnetic monopoles. Trust me on this. I can explain it to you with total clarity, and without hostility. I'll PM you. Let's talk.

59. Originally Posted by Farsight
DRUM: I saw you wer.. I can explain it to you with total clarity, and without hostility.
Fantastic!

A.) Before anything, define "POLE" of a field, define "sink/source", ok?

B.) How many poles magnetic field of a moving charge has?

C.) Right image, how many magnetic FIELDS do you see, where are they?

60. Originally Posted by DRUM
So, yes, just like electric monopoles, it can be both sink and source.
Whoa... Um, an electric monopole is either or, not both. An electric charge that is negative is a source, while a positive charge is a sink. That's the way it is, and in terms of having a single 'sign' charge that's the way it is, always.

61. Originally Posted by Arcane_Mathematician
Originally Posted by DRUM
So, yes, just like electric monopoles, it can be both sink and source.
Whoa... Um, an electric monopole is either or, not both. An electric charge that is negative is a source, while a positive charge is a sink. That's the way it is, and in terms of having a single 'sign' charge that's the way it is, always.
And when you have two positive charges interacting, they repel, yet they're both sinks? So, can you actually write down that definition of yours for "sink/source" or show some links? What happened to my questions to you? What happened with the rest of what I told you, you're ignoring it?

Can you say how many magnetic fields moving charge has? How many poles?

62. The like charges repel while opposing charges attract. if you have two suckers of electric force, they repel, and neither one becomes a 'source' because they are attracting the carriers of electrical energy, not supplying them. your questions to me were asinine, as is your obsession with 'poles'.

The two images you have are looking at the same thing, but from a different perspective. A magnetic field exists in 3 dimensions, and each image is only showing you 2 dimensions of the field. Wikipedia can shed some light on this. And if you go through all those nice links, you'll actually learn a little physics.

63. Originally Posted by DRUM
Originally Posted by salsaonline
Once again, that's not the definition of a magnetic monopole.
What do you think you're doing? Who are you trying to brainwash with that brilliant explanation and convincing arguments? That was general definition for POLE, not magnetic, not monopole, but just 'pole of a field'. It works for gravity fields, electric fields and magnetic dipole fields, ok? -- How did you come up with your conclusion if you can not articulate what do you think 'pole' is and where are they located?

You are not responding to questions:

A.) Is divergence of magnetic dipole zero as well?

B.) How many poles you think this field has, none, one, two, many?

C.) How do you define "POLE of a field"? Is that the same thing as sink/source?
Actually salsaonline is responding to your questions. He is being very precise. Far more precise than your nonsense deserves.

The problem is that you are either too ignorant or simply lack the necessary inate intelligence to recognize that simple fact. Perhaps both.

64. Originally Posted by DRUM

A.) Is divergence of magnetic dipole zero as well?
Yes.

div B = 0

65. Originally Posted by DrRocket
Originally Posted by DRUM

A.) Is divergence of magnetic dipole zero as well?
Yes.

div B = 0
You mean, magnetic dipoles don't have any poles or sink/sources either?

66. Originally Posted by Arcane_Mathematician
The like charges repel while opposing charges attract. if you have two suckers of electric force, they repel, and neither one becomes a 'source' because they are attracting the carriers of electrical energy, not supplying them. your questions to me were asinine, as is your obsession with 'poles'.

The two images you have are looking at the same thing, but from a different perspective. A magnetic field exists in 3 dimensions, and each image is only showing you 2 dimensions of the field. Wikipedia can shed some light on this. And if you go through all those nice links, you'll actually learn a little physics.
Nonsense. There is no sentence in Wikipedia that can support your statements.

"carriers of electrical energy", what in the world is this?!?

67. Originally Posted by DRUM
Originally Posted by DrRocket
Originally Posted by DRUM

A.) Is divergence of magnetic dipole zero as well?
Yes.

div B = 0
You mean, magnetic dipoles don't have any poles or sink/sources either?
Poles are in the eye of the beholder, and depend on your definition.

Physics is not semantics. Learn some physics and forget the semantics. Your physics knowledge is woefully deficient. Virtually nonexistent. In fact it is negative -- what you "know" is just flat wrong.

There are no sources or sinks for magnetic fields. div B = 0

68. Originally Posted by DRUM
"carriers of electrical energy", what in the world is this?!?
IIRC it's the electron...

69. Originally Posted by DrRocket
The problem is that you are either too ignorant or simply lack the necessary inate intelligence to recognize that simple fact. Perhaps both.
Let's limit our criticisms to attacks on assertions rather than on personality. To my mind the red line lies somewhere between suggesting the opponent is ignorant and suggesting he is mentally deficient. I'm guessing you'll disagree, but this is how I moderate.

Drum, as far as I can gather you are failing to accept answers given to your questions and failing to move beyond semantic arguments in your own defence. If that is all there is going to be to this discussion then I'm going to close it, because it's just going to go in circles and the result of that will probably be a flame war. Address the science or I lock.

70. Originally Posted by TheBiologista
Drum, as far as I can gather you are failing to accept answers given to your questions and failing to move beyond semantic arguments in your own defence. If that is all there is going to be to this discussion then I'm going to close it, because it's just going to go in circles and the result of that will probably be a flame war. Address the science or I lock.[/color]
"DivB = 0" only means: "MAGNETIC FIELD LINES ARE CIRCULAR".

I basically proven my point when this bear completely failed to use basic logic and refuted himself with this silly equation by blindly concluding that even DIPOLES do not have any poles! His only argument is obviously very wrong, it's hilarious. Dipoles do have poles, they are called "South" and "North" magnetic poles.

Poles are in the eye of the beholder, eh? Hahahaaaa, oh mercy!

71. Originally Posted by DRUM
Originally Posted by TheBiologista
Drum, as far as I can gather you are failing to accept answers given to your questions and failing to move beyond semantic arguments in your own defence. If that is all there is going to be to this discussion then I'm going to close it, because it's just going to go in circles and the result of that will probably be a flame war. Address the science or I lock.[/color]
"DivB = 0" only means: "MAGNETIC FIELD LINES ARE CIRCULAR".

I basically proven my point when this bear completely failed to use basic logic and refuted himself with this silly equation by blindly concluding that even DIPOLES do not have any poles! His only argument is obviously very wrong, it's hilarious. Dipoles do have poles, they are called "South" and "North" magnetic poles.
It seems to me that his point was that they don't have poles as you are defining them.

72. Originally Posted by TheBiologista
Originally Posted by DrRocket
The problem is that you are either too ignorant or simply lack the necessary inate intelligence to recognize that simple fact. Perhaps both.
Let's limit our criticisms to attacks on assertions rather than on personality. To my mind the red line lies somewhere between suggesting the opponent is ignorant and suggesting he is mentally deficient. I'm guessing you'll disagree, but this is how I moderate.

Drum, as far as I can gather you are failing to accept answers given to your questions and failing to move beyond semantic arguments in your own defence. If that is all there is going to be to this discussion then I'm going to close it, because it's just going to go in circles and the result of that will probably be a flame war. Address the science or I lock.
Don't quote a sentence out of context and then draw a conclusion.

DRUM was given a very precise and correct answer to his question by salsaonline.

His response was not that salsaonline was wrong as a matter of fact, but rather that salsaonline's answer was non-responsive to the question. That is patently false. That leaves only two possible reasons for his conclusion and subsequent attack of salsaonline --the two that I listed.

73. Originally Posted by DrRocket
Don't quote a sentence out of context and then draw a conclusion.

DRUM was given a very precise and correct answer to his question by salsaonline.

His response was not that salsaonline was wrong as a matter of fact, but rather that salsaonline's answer was non-responsive to the question. That is patently false. That leaves only two possible reasons for his conclusion and subsequent attack of salsaonline --the two that I listed.
The context is irrelevant, as is whether I agree with your assessment of DRUM or not. I will not accept ad hominems. Pointing out ignorance can be constructive- if taken on board the user might go and learn more. Suggesting a user is mentally deficient cannot be constructive as no action can be taken to remedy that. The inevitable result of such a suggestion is the degeneration of the discussion. If you have any further problem with my position on this, please discuss it in Feedback, or in a message to myself or an Administrator. I will remove any further off-topic posts from this thread.

74. I request this thread be closed. He's opened the exact same discussion elsewhere, has been refuted on the exact same points by people who are well versed on the topic, and yet he continues with his games.

I understand the desire for decency and civility, I just also recognize when good manners are wasted on a person who is not here to learn, but instead to frustrate membership with silliness and ridiculous refusals to accept valid points and move on.

75. Originally Posted by inow
I request this thread be closed. He's opened the exact same discussion elsewhere, has been refuted on the exact same points by people who are well versed on the topic, and yet he continues with his games.

I understand the desire for decency and civility, I just also recognize when good manners are wasted on a person who is not here to learn, but instead to frustrate membership with silliness and ridiculous refusals to accept valid points and move on.

Request noted. Leaning towards doing so unless things turn around spectacularly in the next couple of posts. Regarding civility, I don't expect ignorance or flawed logic to be given any respect. However this is a discussion forum and we must maintain some basic level of respect if we wish to foster discussion rather than bickering. Aside from creating a hostile atmosphere, it makes my job harder and you see... I am so very lazy.

76. Originally Posted by TheBiologista
It seems to me that his point was that they don't have poles as you are defining them.
He provided no alternative definition, therefore it's pretty clear he thinks magnetic dipoles have no poles just like he thinks magnetic field of a moving charge has no poles. His silly equation simply FORBIDS magnetic poles, sinks and sources. It's because it talks about 'field lines' instead of 'lines of force', simple as that.

I'm using the definition of "pole" as defined in physics, defined by charge magnitude equation (Biot-Savart law) and by the direction of the lines of FORCE (Lorentz force equation), not the direction of field lines. This is the same definition as is used for electric and gravity fields, and the same one used for magnetic dipole fields.

This is the definition of field "POLE":
Pole = extreme, origin, limit, source/sink, point of attraction/repulsion

This is what is meant by any MONO-POLE and DI-POLE:
Di = two, pair --> DIPOLE = two origins, two poles, two source/sinks, two fields
Mono = one, single --> MONOPOLE = one origin, one pole, one source/sink, one field

My opposition not only did not address how and why do they disagree with this definition, but they've never, ever provided their definition. So, would it be fair if they can at least answer these basic questions DIRECTLY:

1.) Define "POLE", "SINK" and "SOURCE".
2.) State how many magnetic FIELDS are depicted on the left and right image.
3.) What is this point inside magnetic field called towards which opposite magnetic fields are attracted to? Is that not sink or pole, is that not the source of magnetic field?

inow,

I find your eagerness to censor public dialog disturbing. Why don't you just ignore it and go elsewhere? You're confusing DEFINITIONS with "semantic game". Of course it's 'semantics' since definitions are constructed from words, but I also gave you mathematical and geometrical description and definitions, as well as experimental measurements.

If you are afraid I can prove laws of physics false by using some magic trick with words, then why don't you provide your definition and we will use that for reference, ok?

- Define field POLE, SINK and SOURCE. Can you do that, please?

77. This explination works well for me. How about you?
Originally Posted by wiki
Magnetic pole model: Although for many purposes it is convenient to think of a magnet as having distinct north and south magnetic poles, the concept of poles should not be taken literally: it is merely a way of referring to the two different ends of a magnet. The magnet does not have distinct north or south particles on opposing sides. If a bar magnet is broken in half, in an attempt to separate the north and south poles, the result will be two bar magnets, each of which has both a north and south pole.

The magnetic pole approach is used by professional magneticians to design permanent magnets. In this approach, the pole surfaces of a permanent magnet are imagined to be covered with so-called magnetic charge, north pole particles on the north pole and south pole particles' on the south pole, that are the source of the magnetic field lines. If the magnetic pole distribution is known, then outside the magnet the pole model gives the magnetic field exactly. In the interior of the magnet this model fails to give the correct field (see #units and calculations, below). This pole model is also called the Gilbert model of a magnetic dipole.[6] Griffiths suggests (p. 258): "My advice is to use the Gilbert model, if you like, to get an intuitive 'feel' for a problem, but never rely on it for quantitative results."

Ampère model: Another model is the Ampère model, where all magnetization is due to the effect of microscopic, or atomic, circular bound currents, also called Ampèrian currents throughout the material. For a uniformly magnetized cylindrical bar magnet, the net effect of the microscopic bound currents is to make the magnet behave as if there is a macroscopic sheet of electric current flowing around the surface, with local flow direction normal to the cylinder axis. (Since scraping off the outer layer of a magnet will not destroy its magnetic field, it can be seen that this is just a model, and the tiny currents are actually distributed throughout the material). The right-hand rule tells which direction the current flows. The Ampère model gives the exact magnetic field both inside and outside the magnet. It is usually difficult to calculate the Ampèrian currents on the surface of a magnet, whereas it is often easier to find the effective poles for the same magnet.
Originally Posted by DRUM
1.) Define "POLE", "SINK" and "SOURCE".
wiki did it for me
2.) State how many magnetic FIELDS are depicted on the left and right image.
only 1 in each, and there exists only 1 magnetic field in each.
3.) What is this point inside magnetic field called towards which opposite magnetic fields are attracted to? Is that not sink or pole, is that not the source of magnetic field?
no, it's not, because in the grand scheme of things, there is only ONE magnetic field in a system, iirc, and salsa or Dr. R can definitely correct me if I'm wrong

78. Originally Posted by Arcane_Mathematician
http://en.wikipedia.org/wiki/Magnet

This explanation works well for me. How about you?

wiki did it for me
Thank you. This is the first direct response.

Unfortunately, no definition of pole there, or sink/source. That bit of text is specifically about the *bar-magnet* and our inability to precisely locate poles because there is many overlapping fields and the total magnitude, hence the point where the magnetic fields are strongest (poles), are smeared around the edges and heavily depend on the shape of the magnet.

Definition has to start with "pole is ....", "sink/source is ..."; it has to be general and has to apply to electric and gravity fields as well, even to vortices, whirlpools and mountains, like this:

2.) State how many magnetic FIELDS are depicted on the left and right image.

only 1 in each, and there exists only 1 magnetic field in each.
Huh??!? Surely, magnetic dipoles have two magnetic fields.

This is like arguing alphabet, so I have no further comments.

3.) What is this point inside magnetic field called towards which opposite magnetic fields are attracted to? Is that not sink or pole, is that not the source of magnetic field?

no, it's not, because in the grand scheme of things, there is only ONE magnetic field in a system, iirc, and salsa or Dr. R can definitely correct me if I'm wrong
Ok, one field, but do we have a name for those points of attraction or not?

79. Originally Posted by DRUM
Originally Posted by Arcane_Mathematician
http://en.wikipedia.org/wiki/Magnet

This explanation works well for me. How about you?

wiki did it for me
Thank you. This is the first direct response.

Unfortunately, no definition of pole there, or sink/source. That bit of text is specifically about the *bar-magnet* and our inability to precisely locate poles because there is many overlapping fields and the total magnitude, hence the point where the magnetic fields are strongest (poles), are smeared around the edges and heavily depend on the shape of the magnet.

Definition has to start with "pole is ....", "sink/source is ..."; it has to be general and has to apply to electric and gravity fields as well, even to vortices, whirlpools and mountains, like this:
I believe you've missed the point, as the article does "define" a pole, just not the way you'd like. It claims a pole is not a literal thing, but for simple reference to the side of a magnet, and the issue we seem to be having is that there doesn't exist a magnet in the universe with only 1 side, hence there is never a net magnetic charge. All particles have both sides of the magnetic charge, there are no magnetically positive nor magnetically negative particles, and so we have no way of having a "monopole" or 'one-sided' magnets.

That is the essence of the simple equation div B=0

Ok, one field, but do we have a name for those points of attraction or not?
I'm sure we do, but I'm unaware of what name that could be.

80. I have to chime in here. All due respect, almost nobody in this thread has a clue what they're talking about, and that includes some of the people arguing against DRUM. I don't mean this as an insult--it just so happens that the concept of a "monopole" involves some subtle mathematical concepts that I think very few people here are familiar with.

I myself would have a hard time giving a precise definition of a monopole without making some reference to de Rham cohomology. The most precise definition of a monopole I can give is that it's a 2-form on R^3--{point} which is closed but not exact. Those familiar with deRham theory will recognize that div(B)=0 implies closedness but says nothing about exactness (unless we're talking about div(B) as a distribution, but let's not go there).

I think that those people who are arguing with DRUM end up doing more harm than good when they don't fully understand the topic themselves. This emphasis on sources/sinks etc is sort of gobbledy-gook--and I don't blame DRUM for remaining unconvinced by it.

81. Originally Posted by salsaonline
I have to chime in here. All due respect, almost nobody in this thread has a clue what they're talking about, and that includes some of the people arguing against DRUM. I don't mean this as an insult--it just so happens that the concept of a "monopole" involves some subtle mathematical concepts that I think very few people here are familiar with.

I myself would have a hard time giving a precise definition of a monopole without making some reference to de Rham cohomology. The most precise definition of a monopole I can give is that it's a 2-form on R^3--{point} which is closed but not exact. Those familiar with deRham theory will recognize that div(B)=0 implies closedness but says nothing about exactness (unless we're talking about div(B) as a distribution, but let's not go there).

I think that those people who are arguing with DRUM end up doing more harm than good when they don't fully understand the topic themselves. This emphasis on sources/sinks etc is sort of gobbledy-gook--and I don't blame DRUM for remaining unconvinced by it.
Without getting into de Rham cohomology the easiest way to talk about this at a relatively elemtary level is in terms of the integral form of Maxwell's equations, which is the way it is normally handled in texts on electrodynamics.

You simply take div B = 0, and (naively) apply the generalized Stoke's theorem (often called the Divergence Theorem in E&M texts) to conclude that the surface integral of the B field over any closed surface is 0. You can start with that form and not have to worry about the subtleties of distributions or deRham cohomology.

If you look at how fields are treated in classical electrodynamics, in practice, this is what is really done.

DRUM's confusion has nothing to do with these subtleties. Remember that he is claiming to produce monopoles using ordinary wire, coils and current.

You are correct in terms of the mathematics, but you are way overthinking this issue.

82. DrRocket:

What you say is true, except for one little subtlety: If q is a point charge with electric field E, then div(E) = 0 away from the locus of the charge. Nevertheless, a point charge still gives rise to a non-zero flux across an enclosing surface. So there's more going on here than a simple application of Stoke's theorem.

I agree that it's possible to explain all of this without making explicit reference to de Rham cohomology. But any explanation you end up giving is going to amount to some sort of discussion about cohomology, even if you manage to avoid explicitly using that word.

Put it this way: Suppose I have a mathematical object g associated to R^3--{point}, and a differential operator d acting on this object. I know that dg = 0, but g is not equal to d(something). Further, I have a pairing between surfaces in R^3---{point} and g, so that (g,S) is not zero whenever S contains the removed point. This is exactly the situation that we have in the case of a static electric charge (or the case of a monopole). We can use whatever terminology we want to describe this set-up (like talking about vectorfields, divergence, and curl, instead of forms and d). But whatever words we use, we're always going to be talking about the same thing--namely cohomology.

83. Originally Posted by salsaonline
DrRocket:

What you say is true, except for one little subtlety: If q is a point charge with electric field E, then div(E) = 0 away from the locus of the charge. Nevertheless, a point charge still gives rise to a non-zero flux across an enclosing surface. So there's more going on here than a simple application of Stoke's theorem.

I agree that it's possible to explain all of this without making explicit reference to de Rham cohomology. But any explanation you end up giving is going to amount to some sort of discussion about cohomology, even if you manage to avoid explicitly using that word.

Put it this way: Suppose I have a mathematical object g associated to R^3--{point}, and a differential operator d acting on this object. I know that dg = 0, but g is not equal to d(something). Further, I have a pairing between surfaces in R^3---{point} and g, so that (g,S) is not zero whenever S contains the removed point. This is exactly the situation that we have in the case of a static electric charge (or the case of a monopole). We can use whatever terminology we want to describe this set-up (like talking about vectorfields, divergence, and curl, instead of forms and d). But whatever words we use, we're always going to be talking about the same thing--namely cohomology.

When Maxwell formulated electrodynamics no one had ever heard of cohomology, or exterior derivatives. Note that I did not say one made a simple application of Stoke's Theorem I said one applied it naively. By naively I mean in the manner that one usually sees it done in physics texts on electrodynamics -- i.e. the integral of the divergence of the D field is the enclosed total charge and the integral of the divergence of the B field is 0. (I am ignoring constants here).

What does div B = 0 mean from the perspective of a physicist ? It is nothing more and nothing less than the assertion, based on experiment, that there is no such thing as magnetic charge, i.e. no monopoles. The origin of Maxwell's equations lies in experiment. No one measures point values. The experimental data is simply that the net flux crossing any closed surface is always zero -- magnetic field lines are closed. This is analagous to the the equation div D = rho which is the assertion that the static electric field is the result of electric charge. There is also some limit experimentally to just how small that closed surface can be, i.e. there is a limit to the smallness of the scale at which the equations actually apply. The mathematics does not recognize this limit, but the physics does.

Now div D = rho also has mathematical subtleties if you consider the effect of a true point charge. But the point charge itself is something of an idealization. The real effect of this is simply that the surface integral of the flux across a closed surface is equal to the enclosed charge. Point charges themselves run into problems, as with the infinte self-energy of the electron, and so ought not be taken too literally -- again we run into the issue of scale at which the theory breaks down. The way to deal with this for the purposes of ordinary electrodynamics is to think of the electron as being slightly smeared out and then only consider closed surfaces sufficiently large to enclose the entire smeared-out electron. This is not completely rigorous, but it does reflect the real physics and it is how electrodyamic calculations are really done.

The point is that there are, as you have correctly recognized, some subtleties required to handle the mathematics rigorously, but those subtleties should not be used to obscure the basic physics. That basic physics quite simply here is the observation that there is no such thing as magnetic charge, at least within the bounds of classical electrodynamics.

The issue as is has been raised pertains quite clearly to classical electrodyamics. It is not an issue of quantum field theory, or Dirac's observation that the existence of even one monopole, anywhere in the universe, would automatically explain the quantization of electric charge.

So div B = 0, interepreted in terms of the basic physics is correct, and it is simply the statement that there are no magnetic monopoles. That is what it has always meant as a member of the Maxwell equations.

84. Div E = 0

Hahahaaa!! We don't even have any electric poles anymore, fantastic.

LINES OF FORCE, draw the magnetic lines-of-force, like you do for electric and gravity fields, and you will see they do point towards magnetic poles as well. Forget the stupid 'field lines' already.

Originally Posted by DrRocket
So div B = 0, interepreted in terms of the basic physics is correct, and it is simply the statement that there are no magnetic monopoles. That is what it has always meant as a member of the Maxwell equations.
No, and "simply" is not an explanation.
It only means: "MAGNETIC FIELD LINES ARE CIRCULAR".

That stupid equation of yours made you blindly conclude even magnetic dipoles do not have any poles!!!

What are the South and North magnetic poles, if not "poles"?

=========================

You two are not qualified to participate in this discussion unless you can tell us what is your DEFINITION of "POLE, SINK/SOURCE". We need to know what in the world are you talking about when you say magnetic North and South poles are not actually poles, so make yourselves clear already:

1.) Define "POLE", "SINK" and "SOURCE".

2.) State how many magnetic FIELDS are depicted on the left and right image.

3.) What is this point inside magnetic field called towards which opposite magnetic fields are attracted to? Is that not sink or pole, is that not the source of magnetic field?

85. Originally Posted by DRUM
Div E = 0

Hahahaaa!! We don't even have any electric poles anymore, fantastic.

LINES OF FORCE, draw the magnetic lines-of-force, like you do for electric and gravity fields, and you will see they do point towards magnetic poles as well. Forget the stupid 'field lines' already.

Originally Posted by DrRocket
So div B = 0, interepreted in terms of the basic physics is correct, and it is simply the statement that there are no magnetic monopoles. That is what it has always meant as a member of the Maxwell equations.
No, and "simply" is not an explanation.
It only means: "MAGNETIC FIELD LINES ARE CIRCULAR".

What are the South and North magnetic poles, if not "poles"?

=========================

You are not qualified to participate in this discussion unless you can tell us what is your DEFINITION of "POLE, SINK/SOURCE". We need to know what in the world are you talking about when you say magnetic North and South poles are not actually poles, so make yourselves clear already:

1.) Define "POLE", "SINK" and "SOURCE".

2.) State how many magnetic FIELDS are depicted on the left and right image.

3.) What is this point inside magnetic field called towards which opposite magnetic fields are attracted to? Is that not sink or pole, is that not the source of magnetic field?

DRUM you have no idea what salsaonline and I are talking about.

You don't even know what you are talking about.

There is no such thing as magnetic charge or magnetic monopoles.

86. Originally Posted by DrRocket

DRUM you have no idea what salsaonline and I are talking about.

You don't even know what you are talking about.

There is no such thing as magnetic charge or magnetic monopoles.

My angry friend, if you can not define your terms and answer these simple questions directly, then obviously it is you whose knowledge is dubious and under suspicion.

1.) Define "POLE", "SINK" and "SOURCE".

2.) State how many magnetic FIELDS are depicted on the left and right image.

3.) What is this point inside magnetic field called towards which opposite magnetic fields are attracted to? Is that not sink or pole, is that not the source of magnetic field?

87. DrRocket:

It's important not to gloss over or explain away the fact that div(E)=0 outside the locus of a point charge. This, after all, is the reason why charge is conserved.

And as long as we're confining ourselves to studying classical electrodynamics, I don't see why point charges are any more problematic than "smeared out" charges. Either approach involves the stipulation of some sort of mathematical model.

88. Originally Posted by DRUM
Div E = 0

Hahahaaa!! We don't even have any electric poles anymore, fantastic.
Salsa, DrRocket and Arcane are putting some real thought, time and effort into their arguments. At least have the decency to respond in kind. Ditch the attitude. Idiotic laughter and sarcasm will make me cross and the result of that will be that you don't get to present your ideas here.

89. Originally Posted by salsaonline
DrRocket:

It's important not to gloss over or explain away the fact that div(E)=0 outside the locus of a point charge. This, after all, is the reason why charge is conserved.

And as long as we're confining ourselves to studying classical electrodynamics, I don't see why point charges are any more problematic than "smeared out" charges. Either approach involves the stipulation of some sort of mathematical model.
div E= 0 in any region in which there is zero charge density. I don't think anyone is glossing over that fact. That simply implies that if you take the surface integral of E over the boundary of any region in whch there is zero charge density you get zero. I see no problem.

You don't really need a point charge for this, only a non-zero charge density.

The only major reason that point charges are more of a problem than smeared out charges is that to deal with them you need distributions or atomic measures and that is generally beyond the level of the people to whom a text on electrodynamics is directed. They know how to integrate density functions, but probably not measures. They almost certainly do not know how to differentiate distributions.

There is the problem that the self-energy of a point charge is infinite. This is usually handled by modeling the electron (at least temporarily) as a sphere of the "classical electron radius" (see e.g. Jackson). So far as I know this issue remains an issue in QED. I think one can ignore this problem for the purpose at hand. It does serve to show that there are some issues with strict mathematical consistency of even classical electrodynamics.

90. Originally Posted by TheBiologista
Salsa, DrRocket and Arcane are putting some real thought, time and effort into their arguments. At least have the decency to respond in kind. Ditch the attitude. Idiotic laughter and sarcasm will make me cross and the result of that will be that you don't get to present your ideas here.
What respect do you have for their "time and effort" if they just told you magnetic dipoles do not have poles?

They do not even understand what is Div F = 0 all about. It's about charge magnitude, uniform 1/r^2 gradient and closed surface, but you need to follow the gradient/slope direction, not field-lines, to find out where are the sinks/sources aka poles or points of attraction/repulsion.

I think this is hilarious. Why not use the same definition and procedure we use to figure out electric and gravity poles? LINES OF FORCE, draw the magnetic lines-of-force, like you do for electric and gravity fields, and you will see they do point towards magnetic poles as well. Forget the 'field lines' and divergence already.

Why change the definition?

91. Originally Posted by DrRocket
div E= 0 in any region in which there is zero charge density.
That's wrong, there is no such region. But, what is this?! Is this trolling? What are you doing in my thread if you are blatantly refusing to answer my questions?

0.) What are magnetic North and South poles, if not poles?

1.) Define "POLE", "SINK" and "SOURCE".

2.) State how many magnetic FIELDS are depicted on the left and right image.

3.) What is this point inside magnetic field called towards which opposite magnetic fields are attracted to?

92. Originally Posted by DRUM
Originally Posted by DrRocket
div E= 0 in any region in which there is zero charge density.
That's wrong, there is no such region. But, what is this?! Is this trolling? What are you doing in my thread if you are blatantly refusing to answer my questions?
I'm ignoring you, and your silly notions.

93. Originally Posted by salsaonline
DrRocket:

It's important not to gloss over or explain away the fact that div(E)=0 outside the locus of a point charge. This, after all, is the reason why charge is conserved.

And as long as we're confining ourselves to studying classical electrodynamics, I don't see why point charges are any more problematic than "smeared out" charges. Either approach involves the stipulation of some sort of mathematical model.
I suggest the simplest logic - lines of force - just like with other fields. Perhaps, for some reason, you can not see my point the way I explain it, so here is Wikipedia 'talk page' where you can find more along the lines of DivE=0 and DivB=0.

http://en.wikipedia.org/wiki/Talk:Ma...ll_original.3F

DrRocket,

Ignorance is bliss, eh?

94. Originally Posted by DRUM
Originally Posted by TheBiologista
Salsa, DrRocket and Arcane are putting some real thought, time and effort into their arguments. At least have the decency to respond in kind. Ditch the attitude. Idiotic laughter and sarcasm will make me cross and the result of that will be that you don't get to present your ideas here.
What respect do you have for their "time and effort" if they just told you magnetic dipoles do not have poles?
I have made my position clear. If you disagree with it, you can bring that to the Feedback forum or you can notify an Administrator by PM. Any further posts in a similarly obnoxious vein will be removed. Any further arguments with me in this thread will be removed.

95. What, if you don't mind my asking, is the 'locus of a charge'?

96. Originally Posted by Arcane_Mathematician
What, if you don't mind my asking, is the 'locus of a charge'?
It is the location of the charge.

97. Originally Posted by TheBiologista
I have made my position clear. If you disagree with it, you can bring that to the Feedback forum or you can notify an Administrator by PM. Any further posts in a similarly obnoxious vein will be removed.

Any further arguments with me in this thread will be removed.