Can Moving Charges Create a Magnetic Field? A Discussion on Electromagnetism

[turin]

I thought we were talking about a deeper insight, not a mathematical equation. I think that viewing the Faraday tensor as a geometrical object, rather than viewing the E and B fields as 3-vectors, provides deeper insight. I must have misunderstood the issue.

 

[Ambitwistor]

Originally posted by turin
I thought we were talking about a deeper insight, not a mathematical equation. I think that viewing the Faraday tensor as a geometrical object, rather than viewing the E and B fields as 3-vectors, provides deeper insight. I must have misunderstood the issue.

The Faraday tensor provides geometric insight that the E and B fields do not, since it is really a measure of curvature. However, if you're asking about how a changing E field influences a B field, the Faraday tensor doesn't give you any advantages, because you have to decompose it back into the indivdiual E and B fields in order to even define them. The aspect of Maxwell's equations in covariant tensor form that influence this particular aspect of physics is precisely the Ampere-Maxwell portion of the equations.

 

[Fairfield]

Zooby:

You are asking about a matter that I offered a novel opinion on on another thread, I don't know whether you read it, but I'm always happy to repeat own ideas.

To reiterate the idea most simply I will point out that two close, slack, parallel wires carrying same direction currents will attract each other laterally. If I roll the wires up into coils, even just single loop coils, and place them on the same axis, and apply same direction currents, they will again attract each other.

If I now hold the coils in my hands, and try to feel out the source of the forces between the two coils, it will feel like it is coming from the centers of the two coils, rather than directly, wire to wire, from the edges of the coils. A magnetic compass needle (which is the electrical equivalent of a miniature DC carrying coil) will indicate the same thing, But, obviously, nothing electrical or dynamic has changed between the two wires except the spacial, but still parallel, arrangement of the two wires.

But scientists, starting with Oersted, Faraday and Ampere, decided to settle on the apparent force source as a true basic force, although they couldn't separate it from the circular current situations in which it appears, except by arbitrary backward logical extrapolation to a single current carrying wire, or by being hypnotized by compass needles. This, in my opinion, is a misconception which is a carry over from the earlier perception of magnetism as it appears in nature in lodestone and magnets.

In other words, I believe there is only a complication of a single kind of field which is introduced when a current is put in a circle. I will refrain from calling this single kind of field an electric field because an electric field has already been defined as something else (a charge around an un neutralized electron or proton). The two different types of fields may be connected but independent phenomena when an electron current flows. (A layman's view only.)

 

[zoobyshoe]

Originally posted by Ambitwistor Likewise, Maxwell's theory doesn't say "how a changing electric field produces a magnetic field", it just says that when a changing electric field is present, there is a magnetic field.

Ambitwistor,

On the above point: In the case of current flowing in a conductor the only change I see, according to your description of the electric field moving along at drift velocity without kinking, is a change of position. This, by your assessment, should be enough for it to acquire the magnetic properties it acquires, and is analagous to the magnetic properties that would be experienced by something in another frame moving relative to a charged body at rest. If this is not a correct characterization of your understanding, point out where I have misunderstood you.

 

[Ambitwistor]

Well, actually one has to be a little careful in this case: if you consider real, physical conducting wire, the current is a stream of electrons moving past a bunch of atomic nuclei at rest. If you shift into the electrons' rest frame, the electrons are at rest, but you get a moving stream of postively-charged nuclei instead.

This situation is not quite equivalent to a bunch of charges at rest, although it is the case that the magnetic field is just due to the velocity of the moving charges, not to any change in the electric field.

If you want to consider a situation that is truly equivalent to a line of charges at rest, you should consider the magnetic field produced by the current of a free electron beam in vacuum.

 

[zoobyshoe]

All quite fascinating, but not what I was asking.

In the case of current flowing in a conductor pinpoint for me, if you would, what aspect of the electric field is changing such that it fullfills Maxwell"s "when a changing electric field is present, there is a magnetic field." It seems to me that if the field is not kinking, but moving along with the current at drift velocity, the only change the field is experiencing is one of position.

 

[Ambitwistor]

Originally posted by zoobyshoe
In the case of current flowing in a conductor pinpoint for me, if you would, what aspect of the electric field is changing such that it fullfills Maxwell"s "when a changing electric field is present, there is a magnetic field."

As I just said above, current flowing through a conductor is not a case where the magnetic field is due to a changing electric field; it is a case where the field is due to the velocity of the moving charges. That's the point of what I have been saying.

In Maxwell's equations, current directly is a source of the magnetic field, just like charge directly is a source of the electric field. In addition, a changing electric field can also produce an magnetic field, and a changing magnetic field can produce an electric field --- but changing fields are not necessary to produce either an electric or magnetic field.

It seems to me that if the field is not kinking, but moving along with the current at drift velocity, the only change the field is experiencing is one of position.

If you postulate an infinite, perfect wire with current moving at a uniform drift velocity, there isn't a change in field at all: the electric and magnetic fields are static.

 

[zoobyshoe]

Originally posted by Ambitwistor
As I just said above, current flowing through a conductor is not a case where the magnetic field is due to a changing electric field; it is a case where the field is due to the velocity of the moving charges. That's the point of what I have been saying.

This does seem to be the point of many of your statements. I perceived an apparent contradiction between this and your report of what Maxwell said. I am trying to get that cleared up in my mind.

In Maxwell's equations, current directly is a source of the magnetic field, just like charge directly is a source of the electric field. In addition, a changing electric field can also produce an electric field, and a changing magnetic field can produce an electric field --- but changing fields are not necessary to produce either an electric or magnetic field.

This, I must ponder.

If you postulate an infinite, perfect wire with current moving at a uniform drift velocity, there isn't a change in field at all: the electric and magnetic fields are static.

This last seems to contradict something you said earlier:

Originally posted by Ambitwistor Also, I did not interpret a charge moving at constant velocity to be "moving with respect to its electric field" -- it carries its electric field along with it, with no "kinks".

I understand that you are saying there is no change in the shape of the field, but did you mean that the field was not moving along with the drift current n the example of the infinite, perfect wire?

 

[Ambitwistor]

Originally posted by zoobyshoe I understand that you are saying there is no change in the shape of the field, but did you mean that the field was not moving along with the drift current n the example of the infinite, perfect wire?

The field in the case of an infinite wire is completely static: it looks exactly the same at any time. For a point charge, the field "moves along with the charge, but keeps the same shape".

(Technically, it doesn't make sense to speak of a field "moving", but what I mean is that the field will have the same "shape", except that it translates with the velocity of the charge, i.e. E(x+vt,y,z;t) = E(x,y,z;0) for a charge moving at speed v in the +x direction.)

 

[zoobyshoe]

OK. I think I understand what you are saying. (Didn't follow the equation, but do go into it now.)

What, then, made the wire twirl around the magnet in Faraday's experiment with the wire, magnet, and mercury?

 

[Ambitwistor]

I don't know that experiment. Can you describe it?

 

[zoobyshoe]

I'll try.

He had a dish of mercury. Pushed up through the center of the dish was one pole of a permanent magnet. Obviously the hole through which the magnet came was sealed off so that the mercury wouldn't run out - say with wax.

Suspended over the dish was a copper wire. This wire hung vertically, by a loop, from a copper horizontal member. It was just large enough in gage to be stiff, not flexible. It hung low enough that it entered the mercury at its bottom end. The loop from which it hung was large enough to allow it to swing in a circle.

Faraday connected one pole of a battery to the mercury, and the other to the horizontal copper cross member. The current then flowed through the cross member to the hanging wire, down the wire into the mercury, then back to the battery.

The hanging wire began twirling as fast as it could around the pole of the magnet sticking up through the mercury. As far as anyone knows this was the first electric motor.

You can make the same set up with salted water instead of mercury.

 

[Ambitwistor]

Okay, I get it. The wire twirls because a magnetic field (in this case, of a permanent magnet) exerts a force on a current-carrying wire. The force is always perpendicular to both the field and the current, which given the geometry of the experiment, makes the wire trace out a circle in the mercury. This force is due to the ordinary Lorentz force law for a charge moving in a magnetic field: F_B = qv x B. It doesn't require a changing field.

 

[QuantumNet]

Two charges moves in the same speed and direction.
Seen from our referencesystem, the electric force between the charges
gets weaker the faster they move due of the magnetical force.
Seen from another valid referencesystem
moving in the same speed and direction as the charges,
there is no magnetical force.
The magnetical force is a relativistic effect.
both the charges are relativistic.

You have to visit http://www.quantumnet-string.tk

 

[zoobyshoe]

Originally posted by Ambitwistor
Okay, I get it. The wire twirls because a magnetic field (in this case, of a permanent magnet) exerts a force on a current-carrying wire. The force is always perpendicular to both the field and the current, which given the geometry of the experiment, makes the wire trace out a circle in the mercury. This force is due to the ordinary Lorentz force law for a charge moving in a magnetic field: F_B = qv x B. It doesn't require a changing field.

You may not believe it, but this explanation of the results Faraday got makes perfect sense to me.

(I don't get the sub B after Force, though)

Edit:It seems to me that the explanation of the behaviour of magnetic poles in permanent magnets must also lie in this same Lorentz equation, with the magntic field of one magnet producing the same perpendicular forces on the moving charges in the other magnet (at least those whose spin is uncompensated) but I can't visualise just how at the moment since these charges would be revolving rather than traveling in a straight line. (It could be that's just whacky thinking, though.)

 

[zoobyshoe]

Back to this:

Originally posted by Ambitwistor
The field in the case of an infinite wire is completely static: it looks exactly the same at any time.

I would like to be able to pin you down about this. Looking exactly the same at any time, doesn't necessarily mean there is no motion. When you say the field in this case is completely static I can understand that there is no change in its intensity, or change in its shape. Yet it seems logical to assume the field is, in fact, flowing down the wire at the drift velocity of the current.

For a point charge, the field "moves along with the charge, but keeps the same shape".

This being the case, it seems logical to conclude that the electric field around the perfect wire, which is the sum of all the electric fields of the point charges that constitute the current, is traveling along with all the point charges as they move along the wire. However, you call this notion into question when you continue with:

(Technically, it doesn't make sense to speak of a field "moving",

You are trying to be careful about not being ambiguous here, which I appreciate, but I'm not grasping why it doesn't make technical sense to speak of a field moving.

but what I mean is that the field will have the same "shape", except that it translates with the velocity of the charge, i.e. E(x+vt,y,z;t) = E(x,y,z;0) for a charge moving at speed v in the +x direction.)

Here you bring in the word "translates". This seems to be the term you would prefer to any form of the word "move" in regard to a field. I am sure there must be important differences between these two terms which make you want to use one rather than the other. You include the equation as an illustration of this translation (I think). So, it seems obvious to me that I'm not going to grasp this situation with the perfect wire without a good understanding of the concept of "translation" as it is used in this situation. Can this be explained verbally, or do I need to be conversant with all the equations?

 

[Ambitwistor]

Originally posted by zoobyshoe
I would like to be able to pin you down about this. Looking exactly the same at any time, doesn't necessarily mean there is no motion. When you say the field in this case is completely static I can understand that there is no change in its intensity, or change in its shape. Yet it seems logical to assume the field is, in fact, flowing down the wire at the drift velocity of the current.

If you can define an experiment by which I can measure that a field is "flowing down the wire", whatever that means, then I might say that the field flows down a wire. But since any measurement of the field at any point with give the same value at any time, I don't know how you're going to do that.

You are trying to be careful about not being ambiguous here, which I appreciate, but I'm not grasping why it doesn't make technical sense to speak of a field moving.

I don't know of a technical definition of what it means for a field to "move", in the sense that, say, a particle moves.

Here you bring in the word "translates". This seems to be the term you would prefer to any form of the word "move" in regard to a field.

Saying that the field "translates" has a mathematically precise definition, which I gave: the field value at a point x at a time 0 is the same as the field value at a different point x+vt at a later time t.

However, by this definition, we cannot define a velocity by which a static field translates.

 

[Fairfield]

Originally posted by Ambitwistor
If you can define an experiment by which I can measure that a field is "flowing down the wire", whatever that means, then I might say that the field flows down a wire. But since any measurement of the field at any point with give the same value at any time, I don't know how you're going to do that.

Zooby and Ambitwister:

It seems to me you just have a semantic problem going on here. The shape of the field around a steady current (or otherwise) is one detectable phenomenon. What's going on under that shape is another detectable phenoenon.

 

[Fairfield]

I would like to add a comment to this thread which may or may not be helpful.

In studying magnetism, It seems clear to me that a problem arises from misconstruing what a compass needle really is indicating when it is placed near a straight current. The name magnetism was originally applied to certain objects which could display MUTUAL attraction or repulsion with a measurable FORCE. You, therefore, can't have real magnetic lines of force without two such objects. Therefore, to apply this title to something which (supposedly) circles a current carrying wire, but doesn't have two objects to refer this force to, redefines the meaning of the phrase "magnetic lines of force" in midstream. This redefinition follows from falsely assuming that any active magnetic compass needle indication always refers to true magnetic lines of force. This is absolutely not true.

To explain this inadvertent switch in the meaning of the phrase, "magnetic lines of force", as it is applied to a straight wire current, we have to consider what the true definition of magnetism originally referred to, and therefore, should continue to refer to, unless formally redefined.. The term "magnetism" was originally applied to objects which, unknown to everybody at the time, contain looped currents for there particular force manifestation, which, therefore, have, spatially speaking, no less than two opposing parallel currents in them (opposite edges of the loop or coil). Since a straight wired current in no way has a either a loop, or two opposing currents, it, does not qualify as a magnetic object which can generate any magnetism, or real magnetic lines of force.

The situation of a compass near a straight current is a different kind of relationship (easily explained) than between two genuine magnetic objects (of which the compass needle can be one of them). The compass needle therefore, near a straight current, falsely projects, in one's imagination, something to which the original meaning of the phrase, "magnetic lines of force", absolutely doesn't apply.

To have a name (phrase) kicking around in science which has two different meanings is not a helpful thing in my opinion. If the incorrect name, "magnetic lines of force", for this particular situation (compass indication near a straight current) has been incorporated into so many physics formulas that it can't be extricated, or if it is used in a monitoring/calculating reference system, then I suggest that, at least, the name of the indicated lines be changed to "Oersted's north-south lines" (OF NO FORCE), and the term "electromagnetic waves" be changed to "electro-Oersted waves". It would be even better, but a mouthful, to call these compass indicated "north-south" lines around a straight current, "Oersted's right angle current direction indicators", because they are simply derived from that by the physioelectric response of a (equivalent) loop current near a straight current, depending on the straight current's direction. This kind of physioelectric effect between current carrying wires should be called Ampereism instead of magnetism (see below).


Further, you also can't have those, "lines of magnetic force", (in diagrams) around the individual wires of a current carrying coil because you ONLY get genuine magnetism off the end of a loop or a coil as a MUTUAL resultant force from the two sets of opposing parallel currents, one set in each magnetic entity, when they are brought near each other. The vector amount of this force varies with different orientations between any two magnetic entities. Aside from that coil, (mostly) "end" effect, you don't have any other genuine magnetic lines of force present Only 'Oersted's lines of NO FORCE' "around" the single internal wires. These lines of no force, naturally cannot be added up to create a net force.

Since genuine magnetism requires at least two parallel opposing currents in each magnetic entity, it is clear that magnetism is a more complex arrangement of a more simple force system relating to the physical reactions between close parallel currents. Since it was Andre M. Ampere who first discovered this physical reaction between close parallel currents, it would seem proper to call this system, Ampereism, and the forces operating there, Ampere's lines of force.

From the above considerations, it appears to me that the overall problem of properly relating magnetism to electricity is that magnetism is a superstructure forces relation system built up of a lower order forces relation system, which latter system should properly be called, Ampereism. Therefore magnetism provides only a confusing view of electro-Ampereism.

What both the loop currents and the straight currents have in common is they both have inductive fields which the working physicist and electrical engineer need to keep track of in order to get a mathematical hold on either field's electrical and physical effects. But it is not helpful to drag around confusing names. A straight wire current's inductive field (Ampereic field) is just that. It is not a loop current's inductive field, so it is not a magnetic inductive field. A magnetic inductive field is a resultant of at least two ampereic fields (spatially speaking). If a common name is going to be used for both types of inductive fields, and the lines for their (flux) densities, it should obviously be Ampereic flux density instead of magnetic flux density.

Fairfield