Classic Electromagnetism

Ambitwistor

Yes, that's the idea.

Charge is invariant, just like mass is. Charge density increases by a factor γ = 1/√(1-(v/c)²), because there is length contraction by a factor γ along the direction of motion, shrinking the volume and increasing the density.

It sounds like they're talking about the modern definition of mass, which is to say that it is invariant. There is also relativistic mass, which some people call mass, which has an extra γ implicitly in its definition; if you use invariant mass instead, then that γ factor is explicitly lying around, but it comes from 4-velocity, so maybe that's what they're talking about.

It can't. Electromagnetic waves are described this way, as a propagating "kink" in the electromagnetic fields. Look at these diagrams:

http://www.chem.yale.edu/~cas/jenkins.html

Electromagnetic waves (both changing electric and magnetic fields) are generated when a charge is accelerated.

turin

Just don't forget that you have to put them together in an object alot like a matrix, called a second rank 4-D tensor. A simple vector just won't do anymore. Then, you have something alot like a matrix operating on a vector that gives you another vector as the force.

(2) The relativistic charge density is the rest charge density multiplied by the γ factor (if I remember correctly).

(3) I agree with this, but it is apparently still quite popular to speak of the mass as a component of a tensor (the time-like component of the four-momentum). It is almost the same thing with charge, but charge density really. The charge density is the time-like component of the electric four-current. By charge density, I mean, that part of the electric four-current that effects the electric field components of the Farady tensor, as opposed to the magnetic field components.

zoobyshoe

This is the point of contention. The illustration presented at the site you linked to shows the stationary particle with radiant lines that are supposed to represent both electric and magnetic lines. That is: the charged particle is radiating two completely different kinds of lines of force when at rest. Thus, according to that site, when the particle is accelerated, both kinds of energies are "kinked", but the kink in the electric field doesn't have anything to do with the magnetic properties of the field created .
Is this how you understand it?

Ambitwistor

When you accelerate a charge, the changing electric field generates a changing magnetic field, which in turn generates a changing electric field, etc., to produce an electromagnetic wave.

However, it is a mistake to claim that all of magnetic fields are produced from changing electric fields, or are related to waves, or something like that. Consider electrostatics and magnetostatics.

And no, the "radiant lines" in the linked site's figures do not represent both electric and magnetic fields. It was a diagram of just the electric field. The magnetic field of a moving point charge isn't radial at all. For that matter, a charge at rest doesn't radiate a magnetic field at all (unless you're including an intrinsic magnetic moment due to its spin, which I'm not; I'm just considering a classical point charge).

zoobyshoe

You say the changing electric field generates a changing magnetic field. We start with electric, how is it transduced to magnetic?
Give me some examples of magnetic fields which are not produced from changing electric fields.
,
The word "kinks" used at the site is acceptable.
I'm not sure how electrostatics
supports your point, and I've never heard of magnetostatics so you'll have to fill me in to the extent it's necessary to understand how it supports your point.
Thank God.
This last concurs with what I already thought to be true.

Ambitwistor

Ampere-Maxwell's law: a changing electric field induces a magnetic field.

The magnetic field of a charge moving at constant velocity.

Electrostatics is the special case of electromagnetism when the electric field is static. Magnetostatics is the special case when the magnetic field is static. There are no wavelike, propagating disturbances in such fields: that's the definition of "static" (unchanging with time).

zoobyshoe

This is simply a description of what happens, not an explanation of how it happenes.

The magnetic field of a charge moving at constant velocity.

This is in conflict with what you said earlier, that a magnetic field only arises from acceleration. You said it was misleading of me to say it arose from simply "moving" the particle.
I've never heard it described as a special case of electromagnetism, and I still don't see where it supports your point.
I understand the concept,then, but you are ignoring the fact that non-varying magnetic fields are being generated by constantly moving charged particles. The initial question was about this basic kind of field, not oscillating fields. The static field around a wire carrying current results from the moving charges in that wire. Likewise the static field around a permanent magnet results from the electrons in the material constantly moving around tiny circuits in the magnetic domains.
The magnetic fields, in these situations, are in fact "kinks" in the electric field.

Ambitwistor

Fundamental physical theories always explain what happens, not "how it happens". Gravity doesn't say "how mass produces a gravitational field", it just says that when mass is present in some amount, there is a gravitational field. 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.

I never said that. In fact, I specifically said the opposite: that electromagnetic radiation from accelerating charges doesn't account for all magnetism.

It seemed were implying that magnetic fields always arise from changes in the shape of the electric field, as when you accelerate a charge. That's what I called misleading; it is not true for the magnetic fields arising from a charge in inertial motion. Rather, the electric field in one frame transforms to be a partly electric and partly magnetic field in another frame. The fields do not change shape in this situation.

What, electrostatics?? Magnetostatics?? Electrostatics and magnetostatics are what you get when you set the time derivatives in Maxwell's equations to zero: that's the very definition of "electrostatics" and "magnetostatics".

What did you think the definition of "electrostatics" was?

The point is that in an electrostatic or a magnetostatic situation, there are no waves, and no changing fields. So your statement, "A magnetic field is an electric field with transverse waves in it" cannot be true.

That's my point!! You were the one who was claiming that a magnetic field is "an electric field with waves in it". But there are certainly cases of magnetic fields where no waves are involved.

zoobyshoe

My question was how does the electric field create the magnetic field. Simply restating that it does is not an answer. Then evading my objection to that by saying physical theories always explain what but not how is also not an answer. If you don't know just say so. GR says that mass creates gravity by curving the Space-Time around it. Here is what you said:
So, I stand corrected, you did not say accelerating a charged particle was the only way to create a magnetic field. I did say that magnetic fields are created when charged particles move relative to their electric fields. I did not imply this was the only way. Kartiksg asked if it were possible that an electric field might seem like a magnetic one from another frame of reference. I said that was an important question, and I restated it, paraphrasing it, meaning: I did not know the answer but wanted to find out. This is in my post 11-02-2003 03:07 AM
I thought the definition of "electrostatics" was the study of the behaviour and properties of charges at rest. I still do. I wasn't commenting on the definition of electrostatics, I merely said I had never heard it classified as you classified it. Since I am willing to abandon the word "waves" in favor of "kinks" I hope you will be satisfied. If by the latter you are refering to the basic static field around a current carrying conductor, or a permanent magnet then I still am in disagreement. The magnetic field in them is created as I described it to be. We may call the disturbances in the electric field "kinks" instead of waves because my sence is that you will only accept "waves" in the case of electromagnetic radiation resulting from oscillation of the polarity of a magnetic field. But in permanent magnets and current carrying conductors the "kinks" are in constant motion away from the source at C and are constantly being replaced by more of the same as the charged particles continue to move.

Ambitwistor

I am not evading your question. The laws of physics do not state "how a changing electric field creates a magnetic field".

GR does not specify "how" mass produces spacetime curvature, and EM theory does not specify "how" a changing electric field produces a magnetic field. GR just gives an equation that says if some amount of mass is present, then some amount of curvature will also be present: it doesn't specify a mechanism. EM theory just gives an equation that says if an electric field is changing at some rate, a magnetic field will also be present: it doesn't specify a mechanism.

It seemed to me that you did, when you said that magnetic field was an electric field with waves in it. 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". But if that's not what you mean, then I misinterpreted.

There are no "kinks" in the electric (or magnetic) field of a point charge in uniform motion. So it seems we are still in disagreement that magnetic fields represent "kinks" in the electric field.

There are no "kinks" in the field in these cases either -- the fields are static, and carry no propagating changes, wavelike or otherwise, at speed c or otherwise. At least, not if they're ideal current-carrying conductors or magnets (i.e., they dissipate no energy).

zoobyshoe

I believe the whole point of explaining how the field becomes kinked when the charge is accelerated is to explain the exact mechanism whereby the electric field takes on different properties that manifest as magnitism.
Each new level of understanding about the "how" can beg the next question. It is quite likely we'll never get to the last "how" question,concerning any phenomenon. With gravity, to assert that the mere presence of mass curves the space-time around it is to specify a mechanism. It is a huge step in explaining how gravity works: It specifies that mechanism as opposed to something else , (like an attractive force, or a pushing force.)
It does seem logical to conclude that a charge moving with uniform velocity would carry a uniformly shaped field along with it. I'm not sure this situation can exist, and if it can it isn't what is going on when current moves in a conductor or when electrons orbit in a permanent magnet.
I'll need an example of a situation of a point charge in uniform motion.
We should expect to find kinks in the electric fields of all the electrons that are moving in a current-carrying conductor and of all those moving in a permanent magnet because the motion of these particles is not straight line uniform motion. These electrons are constantly in circular motion and therefore are constantly undergoing centripetal acceleration.
The field as a whole can be regarded as "static" only in the sence there is no change in its intensity or polarity, but the field itself arises from the constant changes in the positions of the electrons whose electric fields are the basis of the magnetic field. The change in position is an acceleration in this case, and since we are already agreed on kinks arising in cases of acceleration of charges, I hope we can agree on kinks in this case of acceleration of charges.

Ambitwistor

It's easy to describe the kink in the electric field, but if you want to describe "how" a changing electric field generates a magnetic field, you're not going to get a deeper answer than the Ampere-Maxwell law, just like for gravity you're not going to get a deeper answer than the Einstein field equation.

I agree with that.

Well, perhaps you and I disagree as to what constitutes a "mechanism". But either way, I don't see why you think that "the presence of mass creates spacetime curvature" (Einstein field equation) specifies a mechanism, but "the presence of a changing electric field creates a magnetic field" (Ampere-Maxwell law) does not.

??? Look at a charge at rest. Switch to a uniformly moving frame. Or look at a cosmic ray travelling through vacuum -- it's near enough to linear motion.

Yes, it is what goes on when electrons move in a conductor: they move along the wire at a constant drift velocity. (Well, an ideal conductor, anyway. In a real conductor, they will get scattered around some, and there will be a little bit of electromagnetic radiation. This is negligible to understand the magnetic field generated by the current.)



In a wire, the electrons do move in straight line uniform motion.

In a permanent magnet, electrons can sort of be thought of as classically moving around in circles. (Although this is not the whole reason why atoms in a magnet can have a magnetic moment; there is also the intrinsic magnetic moment.)

Classically, this system would radiate electromagnetic waves, so changes in the field would propagate outward as "kinks" at the speed of light, carrying energy away from the system.

However, quantum mechanically, this radiation does not happen -- the fields are static, nothing propagates away. (That's why atoms don't collapse.)

It's true that the electrons accelerate. But this is not a case where the magnetic field arises from changes in the electric field; the best classical analogue is that of a current loop, which generates a static field.

Look: whenever "kinks" in the field propagate, they always carry energy away. The mechanical system loses energy. No system that doesn't "run down" can have them (unless it's continually receiving energy from outside, like if it's in thermal equilibrium with the environment). That includes charges in inertial motion, current in an ideal, resistanceless wire, electrons in atoms, and permanent magnets. All those systems have fields with no propagation, (except for the non-ideal case of thermal radiation, which in any case is not responsibile for the vast majority of their magnetism).

Fairfield

Zooby:

Did you catch that it is acceleration relative to an EMF that produces an electromagnetic wave, not Newtonian spacial acceleration? A constant current in a coil (with a circular EMF), although changing position relative to Newtonian space, does not radiate energy. But a constant current there, or anywhere, maintains a constant field there including a (claimed) circular component around the current called: magnetic.

zoobyshoe

I'm not dead. I'm thinking about this.

turin

Might I suggest the Farady tensor as a deeper answer?

Ambitwistor

No. The Faraday tensor is just a way of encapsulating the electric and magnetic fields. To determine how a changing electric field relates to a magnetic field, you need the field equations, which are Maxwell's equations, of which one is the Ampere-Maxwell equation -- regardless of whether you choose to write them in terms of E and B, or F.

turin

Actually, E and B are not tensors, but F is. If you mean that the Faraday tensor just serves an organizational purpose, then I disagree with that. It is my understanding that a tensor is a deeper object than even its own representation (in this case, the 4x4 matrix that encapsulates the components of the electric and magnetic fields). In Fact, the four Maxwell's equations just reduce to two tensor equations. One of these equations contains the relationship between the changing electric field and the resulting magnetic field. It is not so disjointed as some integral equation that expresses the magnetic field as the result of a changing electric field, but a statement that the Faraday tensor is a geometric object in space-time, independent of representation in space-time.

If you meant "the Ampere-Maxwell equation" as the tensor equation, then I guess I do agree. But I interpretted you to mean one of the four Maxwell equations.