Classic Electromagnetism

[kartiksg]

Hi,

I would like to clarify some points on electromagnetism. Most (if not all) of my teachers say that moving charges create a magnetic field. I would just like to know... relative to what? If two electrons move parallel to each other with the same velocity, would they show any magnetic interaction?

Furthermore, my prof.s also say "Current creates a magnetic field. When a current flows in a conductor, electrons are flowing in them, this creates the field" Again.. electrons are 'flowing'... does that mean the magnetic field is created due to the acceleration (electrons do accelerate across a potiential difference right?) or is it due to the drift velocity as it is. If it is the drift velocity, then shouldnt wires of differnet mterial produce different magnetic fields? Also, we know the Lorentz formula
F = q(E + vxB) - what is the v relative to? for. eg. If I take a stream of electrons that are accelerating with constant acceleration 'a' from x=-[oo] to x=[oo], then all inertial frames that move parallel (or antiparallel) to this stream describe the stream (i.e, parallel to x axis) in the same manner. So how do I decide what the 'v' in Lorentz equation is?

Also, is there any way of absolutely distinguishing between an electric and magnetic field? Is it possible that an electric field in one frame might appear like a magnetic field in another? I was thinking of motional emf and its field when I wrote the previous line... it can be thought of on the basis of magnetic field, but it is an electric field as well ( I think... ).Is it possible to describe all magnetic effects on the basis of induced (mebbe imaginary) electric fields alone?

In replies, please use mathematics or formal theoretical framework wherever possible but.... Im in high school ok [;)]

Thanks for any help

Kartik

[sridhar_n]

Yes, Magnetic Fields are created by accelerated charges and no An Alectric field in one frame is not seen as a Magnetic Field in the other.

[sridhar_n]

View this thread (http://www.physicsforums.com/showthread.php?s=&threadid=4820) You will fid ur answers

[kartiksg]

I still dont get how to apply v in the formula. Relative to what? How do I sense the movement relative to a field? Also, according to This site (http://rognerud.com/physics/html/sec_1.html) , it says u can interchange the fields... can someone gimme some feedback on that?

Kartik

[Ambitwistor]

Originally posted by kartiksg
Most (if not all) of my teachers say that moving charges create a magnetic field. I would just like to know... relative to what?

Relative to the observer who sees the charges moving and measures the field.


If two electrons move parallel to each other with the same velocity, would they show any magnetic interaction?

In a frame in which both electrons are moving, yes. In the electrons' rest frame, no: there is no magnetic field in that frame.

(Well, actually yes because they still have an intrinsic magnetic moment, so there is a magnetic field in that frame. But there is no velocity-induced magnetic interaction due to their charges.)


Furthermore, my prof.s also say "Current creates a magnetic field. When a current flows in a conductor, electrons are flowing in them, this creates the field" Again.. electrons are 'flowing'... does that mean the magnetic field is created due to the acceleration (electrons do accelerate across a potiential difference right?)
or is it due to the drift velocity as it is.

It's due to the drift velocity.

If it is the drift velocity, then shouldnt wires of differnet mterial produce different magnetic fields?

Well, if you apply a fixed potential difference, then different wires will have different resistances, thus different currents, thus different magnetic fields.

Remember, the current is related to the drift velocity by,

I = nevdA

where n is the electron density, e is the electron charge, vd is the drift velocity, and A is the cross-sectional area of the wire.

If two materials have different drift velocities, then each individual electron will produce a different magnetic field. But the total magnetic field produced also depends on how many electrons are moving. What matters to the total field, is the the rate at which the total charge is moving: that quantity is called the current.

So, for instance, if you fix the current, then you will have the same magnetic field? How is that compatible with differing drift velocities? Well, the electron densities are different too, and if you physically arrange it so that I is constant, then vd and n always have to vary inversely to make their product a constant.


Also, we know the Lorentz formula
F = q(E + vxB) - what is the v relative to?

It's relative to whatever frame is measuring the force, E field, and B field.

for. eg. If I take a stream of electrons that are accelerating with constant acceleration 'a' from x=-[oo] to x=[oo], then all inertial frames that move parallel (or antiparallel) to this stream describe the stream (i.e, parallel to x axis) in the same manner.

No, different frames will see the electrons moving at different speeds, and thus will measure different charge densities for the streams (Lorentz contraction), different speeds, and different magnetic fields.


Also, is there any way of absolutely distinguishing between an electric and magnetic field?

In a given frame, yes. The electric field in that frame induces a force independent of velocity in that frame.


Is it possible that an electric field in one frame might appear like a magnetic field in another?

Yes! Exactly! Maxwell's theory of electromagnetism is a relativistic theory, even though nobody knew that when it was invented. The electric field and magnetic field are unified into the electromagnetic field: the first "unified field theory". What is an electric field in one frame is generally partly electric and partly magnetic in another, and same for a magnetic field in one frame. Different observers see different E and B fields, which are really just different perspectives of the same unified F (electromagnetic) field.

(Einstein invented special relativity by noticing that Newton's laws of mechanics were inconsistent with Maxwell's theory. Most people tried to keep Newton's mechanics by assuming that Maxwell's theory was only true in one special frame -- the "aether frame". Einstein took the opposite approach, and looked for a new mechanics that would allow Maxwell's equations to be true always -- and invented relativity.)


Is it possible to describe all magnetic effects on the basis of induced (mebbe imaginary) electric fields alone?

More or less. If you start with just Coulomb's law, and require that the laws of electromagnetism obey Einstein's relativity postulates, then you can derive not only magnetic effects but all of electromagnetism.

(Well, I'm lying a little. There are some technical assumptions you have to make, like assuming that the fields can depend on position and velocity, but not acceleration, that they can be derived from a relativistically invariant potential, etc. In section 26-1 of volume II of the Feynman Lectures, Feynman kind of derides people who claim they can derive Maxwell's equations this way because there are a bunch of non-obvious extra assumptions you have to make ... but still, the basic idea is valid.)

To see a "derivation" of Maxwell's equations from Coulomb's law and relativity, see Principles of Electrodynamics by Schwartz. To see how electromagnetic fields transform in different reference frames, see most intermediate or advanced texts in electromagnetism, such as the Feynman Lectures.

[kartiksg]

Thanks... I understood most of it... but I still didnt get the parallel electron part. You said that the magnetic field will exist in the frames where the electrons are in motion. So if in a frame, I see the electron moving with velocity v, I see 2 forces on the electrons
1. Coulombic force (repulsive):- Fe = k e^2 / r^2 where r is the dist of separation and k is the coulomb's constant.
2. Magnetic force (attractive):- Fm... Im not sure what its magnitude will be as I dont know how to calculate the magnetic field produced by an electron... but I know it will be attractive (Using the Maxwell's Grip rule and the Fleming's Left hand rule).

In yet another frame, the observer sees no motion of the electrons. So he sees only the coulomb force.. call this Fe'

Using the first postulate of relativity:

Fe' = Fe + Fm

???

How can this be... I tried asking my teachers (3 of them) this and didt get a good answer...

Is it that the coulomb force is decreasing in the first frame... or increasing in the second.. or is there some other force Im not taking into consideration? ( I suppose u can ignore the effects caused due to the electron spin as they will be common in both... or can u? )

Thanks for the help

Kartik

[kartiksg]

Also, can u elaborate on how different observers will measure different charge densities for the stream of electrons?

Can I also have an equation on how to describe the magnetic field of a moving electron? I have equations for fields of a current - Biot Savart Law.. but none for a single charged particle.. or a system of particles. Also, is there a single equation that describes all the electric and magnetic forces together - simultaneously.. rather than four separate equations - as in maxwell's 4 equations. I read stuff on other threads about the EM field tensor... can someone explain what it is and how I ca apply it?

Thanks

Kartik

[Ambitwistor]

Originally posted by kartiksg

Using the first postulate of relativity:

Fe' = Fe + Fm

This is a mistake. The first postulate does not say that the total force in one frame is the same as the total force in another. (Just like it doesn't say that the field in one frame is the same as the field in another, or the time in one frame is the same as the time in another, ... etc.)

If I find time, I might sit down and work out the transformations and post them, but don't expect that immediately.

[Ambitwistor]

Originally posted by kartiksg
Also, can u elaborate on how different observers will measure different charge densities for the stream of electrons?

Imagine a linear stream of charge. If you boost in the direction of its motion, the boosted observer will see the stream length-contract, so the charge density will increase (the same charge is contained in a smaller volume).

Can I also have an equation on how to describe the magnetic field of a moving electron? I have equations for fields of a current - Biot Savart Law.. but none for a single charged particle..

It's really just another form of the Biot-Savart law:

http://academic.mu.edu/phys/matthysd/web004/l0220.htm

That's for a constant velocity. Things start getting very complicated once you introduce acceleration.

Also, is there a single equation that describes all the electric and magnetic forces together - simultaneously.. rather than four separate equations - as in maxwell's 4 equations.

Yes. In unified form, Maxwell's four equations become two equations, and if you assume that the fields are derived from a potential, one of those equations is a tautology, so the meat of it is in one equation.

In tensor (matrix) form,

∂Fab/∂xa = 4π jb

∂Fbc/∂xa + ∂Fca/∂xb + ∂Fab/∂xc = 0

where F is the field tensor and j is the current 4-vector. (There is an implicit summation over the 'a' index in the first equation. There are also supposed to be some ε0's and μ0's and maybe c's in there somewhere, but I always choose units in which they're equal to 1 so I don't have to worry about them.)

If you assume that the field tensor F is derived from a potential 4-vector A,

Fab = ∂Ab/∂xa - ∂Aa/∂xb

then the second of the equations is automatically true and thus redundant.


I read stuff on other threads about the EM field tensor... can someone explain what it is and how I ca apply it?

It's a 4x4 antisymmetric matrix whose six independent components are the three electric field and three magnetic field components. I don't really want to give a lecture on it, so you should just find a book that discusses electromagnetism in covariant form. Usually you don't bother with it unless you care about transformations between highly relativistic frames or something.

[kartiksg]

Thanks a lot.. the site really helped.... as for those weird looking equations... I guess Ill wait till I get to college and do partial derivatives before I try to get what it meant [;)][:D][6)]

Again, Thanks a ton for the help

Do write about why the forces need not be equivalent in different frames and how they are balanced when u get time.

Kartik

[turin]

Originally posted by kartiksg
... I still didnt get the parallel electron part.
..
... I see 2 forces on the electrons
1. Coulombic force ... Fe ...
2. Magnetic force ... Fm ...
...
In yet another frame, the observer sees no motion of the electrons. So he sees only the coulomb force.. call this Fe'

Using the first postulate of relativity:

Fe' = Fe + Fm

How can this be...
...
Is it that the coulomb force is ... increasing in the second.Yes. (If I understand you correctly). In Newtonian physics, the magnetic force will balance the electric force when the electrons are moving at c parallel to each other (an interesting result, I think). Applying relativistic effects, the equation you suggest will be true. You can look at it two ways: 1) The charge on the electrons will increase (a relativistic phenomenon, kind of like an increase in mass, but different, so don't go around telling people that I said it was the same) the faster they go, thus increasing the electric repulsion, and thus canceling the magnetic attraction 2) You can consider the tensor equation, but that's more sophisticated.

If you know what a vector and a matrix are, then just think of the Newtonian version of the electric and magnetic fields as 3-D vectors and the charge as a scalar. The relativistic version of the electromagnetic field as a 4x4 matrix the charge and current get lumped into one 4-D vector. Then, you operate the 4x4 matrix on the 4-D vector to get the 4-D force.

[Ambitwistor]

As for why the forces aren't the same in different frames... well, it should at least be obvious that the accelerations aren't the same: if two electrons are released from rest and repel each other in one frame, then in a frame moving with respect to that one, there will be time dilation, so that observer will see them repelling more slowly. If you want to talk about forces, we have to get into the relativistic definition of force and how it transforms, but hopefully this acceleration argument will be convincing.

It is possible to construct a 4-dimensional spacetime vector called the "4-force" such that your equation Fe' = Fe + Fm will hold, if those symbols refer to the 4-forces. But the ordinary 3-forces aren't the same in both frames.

I was going to type in a derivation of these effects, but I thought it would be quicker if I could just find a web page that derives it, similarly to how Schwartz or Feynman do it (I think Feynman is, as usual, clearer) ... they consider an electron being repelled from a current-carrying wire, though, instead of two electrons:

http://www.astro.warwick.ac.uk/warwick/chapter3/node3.html

[zoobyshoe]

Originally posted by kartiksg
Hi,

I would like to clarify some points on electromagnetism. Most (if not all) of my teachers say that moving charges create a magnetic field. I would just like to know... relative to what?

A charged particle radiates an electric field. When the particle is moved there is a lag in the time it takes for the field to catch up. There is a difference in the shape of the electric field from the initial position and the succeding positions. The waves created in the electric field by moving the particle generating the field are electromagnetic waves.
So the answer is that charges moving relative to their own electric field create magnetic fields.

[zoobyshoe]

Originally posted by kartiksg Also, is there any way of absolutely distinguishing between an electric and magnetic field?
A magnetic field is an electric field with transverse waves in it. The electric field is always potentially radiant. The waves that cause it to become "magnetic" are at right angles to the radiant vectors of the electric field's potential.
Is it possible that an electric field in one frame might appear like a magnetic field in another?
This is a very important question. If an electric field is stationary relative to the charge from which it emanates, could there be motion in some other frame such that the electric field seems to be possessed of transverse waves propagating at C?
Is it possible to describe all magnetic effects on the basis of induced (mebbe imaginary) electric fields alone?

Electric fields naturally arise from charged particles. There is no way to induce an electric field in a particle. Electrons have one kind of charge, Protons have the other kind of charge, and Neutrons don't have any charge. There doesn't appear to be any way to induce an electric field in a particle that it doesn't already have one, or to change the one it has.

It is true that all magnetic effects arise from the electric field.

[kartiksg]

Hi,

Thanks to all u ppl... Im finally beginning to get the hang of this... E field and B field by themselves arent Lorentz invariant but taken together, they are invariant. Force by itself is not invariant, but the four vector of force is. Thanks.... Thanks a ton.... I am finally beginning to see how 'relative' relativity can actually get [:D].

I have seen the formulae for length contraction, time dilation etc. but havnt seen one for charge increase... can I know how the rest charge differs from moving charge? Also, it was stated in www.modernrelativity.com that the mass by itself remains the same in the transformation between frames and we should associate the [gamma] with the velocity vector.. or sumthing like that. Is is the same thing here with the charge as well? ( Im not sure I phrased that well... ).

Also... if magnetic field can be thought of as the lag of electric field... how do we think of the lag of a magnetic field? Is there something like that? I think that should happen when u accelerate the charge, resulting in a gradual lag of the lag of the electric field [g)]( all tongue twisted.. ).


Thanks

Kartik

[zoobyshoe]

Originally posted by kartiksg Also... if magnetic field can be thought of as the lag of electric field...
This isn't quite right. The electric field itself doesn't lag. There is a lag in the adjustment of its position when you move the source of the field. The lag in the adjustment of it position is extremely small but measurable: it is the speed of light.
how do we think of the lag of a magnetic field? Is there something like that?
I think that should happen when u accelerate the charge, resulting in a gradual lag of the lag of the electric field [g)]( all tongue twisted.. ).
You can't ever accelerate a charge to the speed of light, therefore there is no risk of accelerating it faster than the magnetic field that results from its change of position can propagate.

[Ambitwistor]

Originally posted by zoobyshoe
A charged particle radiates an electric field. When the particle is moved there is a lag in the time it takes for the field to catch up. There is a difference in the shape of the electric field from the initial position and the succeding positions. The waves created in the electric field by moving the particle generating the field are electromagnetic waves.
So the answer is that charges moving relative to their own electric field create magnetic fields.

This is misleading. If a charge accelerates (not just moves), it will emit electromagnetic radiation, which is a self-supporting oscillation of electric and magnetic fields. (And it will create radiation even in the particle's instantaneous rest frame.) But that doesn't account for all magnetism, it just accounts for electromagnetic waves. There are plenty of other magnetic phenomena. The point is not that a changing electric field will produce a magnetic field in some frame; it's that an electric field (changing or not) in one frame is (at least partly) a magnetic field in another frame.


A magnetic field is an electric field with transverse waves in it.

This definitely is not true. You can have electric and magnetic fields without any waves in them at all. I think you're again looking specifically at the case of electromagnetic radiation -- and even then, I wouldn't say that a magnetic field is an "electric field with waves in it".

[Ambitwistor]

Originally posted by kartiksg
E field and B field by themselves arent Lorentz invariant but taken together, they are invariant. Force by itself is not invariant, but the four vector of force is.

Yes, that's the idea.

I have seen the formulae for length contraction, time dilation etc. but havnt seen one for charge increase... can I know how the rest charge differs from moving charge?

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.


Also, it was stated in www.modernrelativity.com that the mass by itself remains the same in the transformation between frames and we should associate the [gamma] with the velocity vector.. or sumthing like that. Is is the same thing here with the charge as well?

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.

Also... if magnetic field can be thought of as the lag of electric field...

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]

Originally posted by kartiksg
(1)
E field and B field by themselves arent Lorentz invariant but taken together, they are invariant. Force by itself is not invariant, but the four vector of force is.
...
(2)
I have seen the formulae for length contraction, time dilation etc. but havnt seen one for charge increase... can I know how the rest charge differs from moving charge?
...
(3)
... the mass by itself remains the same in the transformation between frames and we should associate the [gamma] with the velocity vector.. or sumthing like that. Is is the same thing here with the charge as well?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]

Originally posted by Ambitwistor This definitely is not true. You can have electric and magnetic fields without any waves in them at all.
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]

Originally posted by 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.
You say the changing electric field generates a changing magnetic field. We start with electric, how is it transduced to magnetic?
However, it is a mistake to claim that all of magnetic fields are produced from changing electric fields...
Give me some examples of magnetic fields which are not produced from changing electric fields.
or are related to waves,
The word "kinks" used at the site is acceptable.
Consider electrostatics and magnetostatics.
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.
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.
Thank God.
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).
This last concurs with what I already thought to be true.

[Ambitwistor]

Originally posted by zoobyshoe
You say the changing electric field generates a changing magnetic field. We start with electric, how is it transduced to magnetic?

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


Give me some examples of magnetic fields which are not produced from changing electric fields.

The magnetic field of a charge moving at constant velocity.


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.

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]

Originally posted by Ambitwistor
Ampere-Maxwell's law: a changing electric field induces a magnetic field.
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.
Electrostatics is the special case of electromagnetism when the electric field is static.
I've never heard it described as a special case of electromagnetism, and I still don't see where it supports your point.
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).
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]

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


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.


This is in conflict with what you said earlier, that a magnetic field only arises from acceleration.

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


You said it was misleading of me to say it arose from simply "moving" the particle.

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.


I've never heard it described as a special case of electromagnetism,

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?

and I still don't see where it supports your point.

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.

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.

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]

Originally posted by 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.
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. I never said that. In fact, I specifically said the opposite: that electromagnetic radiation from accelerating charges doesn't account for all magnetism.
Here is what you said:
Originally posted by Ambitwistor This is misleading. If a charge accelerates (not just moves), it will emit electromagnetic radiation, which is a self-supporting oscillation of electric and magnetic fields. (And it will create radiation even in the particle's instantaneous rest frame.) But that doesn't account for all magnetism, it just accounts for electromagnetic waves. There are plenty of other magnetic phenomena. The point is not that a changing electric field will produce a magnetic field in some frame; it's that an electric field (changing or not) in one frame is (at least partly) a magnetic field in another frame.
So, I stand corrected, you did not say accelerating a charged particle was the only way to create a magnetic field. 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.
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
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? 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. 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. Since I am willing to abandon the word "waves" in favor of "kinks" I hope you will be satisfied. 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.
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]

Originally posted by 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.

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


GR says that mass creates gravity by curving the Space-Time around it.

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.


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.

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.


Since I am willing to abandon the word "waves" in favor of "kinks" I hope you will be satisfied.

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.

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.

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]

Originally posted by Ambitwistor
I am not evading your question. The laws of physics do not state "how a changing electric field creates a magnetic field".
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.
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.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.)
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".
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.
There are no "kinks" in the electric (or magnetic) field of a point charge in uniform motion.
I'll need an example of a situation of a point charge in uniform motion.
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).
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]

Originally posted by 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.

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.


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.

I agree with that.

With gravity, to assert that the mere presence of mass curves the space-time around it is to specify a mechanism.

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.


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,

??? 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.

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.

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.)


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.

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.)

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.

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.


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.

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]

Originally posted by Ambitwistor 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).
I'm not dead. I'm thinking about this.

[turin]

Originally posted by Ambitwistor
... 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, Might I suggest the Farady tensor as a deeper answer?

[Ambitwistor]

Originally posted by turin
Might I suggest the Farady tensor as a deeper answer?

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]

Originally posted by 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. 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.

[Ambitwistor]

Originally posted by turin
Actually, E and B are not tensors, but F is.

I never said E and B were tensors.


If you mean that the Faraday tensor just serves an organizational purpose, then I disagree with that.

The electromagnetic field tensor is more fundamental than the electric or magnetic fields, which are frame-dependent quantities. However, if you want to ask a question about how B depends on changing E, then you are going to have to go to a frame: E and B aren't defined otherwise.

In any case, the F itself contains no information about how changes in anything influence anything else; that's what the field equation (Maxwell's equations) is for. Whether you write Maxwell's equations in pretty covariant tensor form, or use differential forms, or geometric algebra, or quaternions, or coordinates, doesn't matter: you're still using Maxwell's equations, and the Maxwell equation that describes how a changing E field affects a B field is the Ampere-Maxwell law, regardless of whether or not you consider it to be unified with other of Maxwell's equations.


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.

There is no Ampere-Maxwell equation as a tensor equation. And the full Maxwell equations, in tensor form or otherwise, don't tell you anything more about how a changing E field affects a B field than just the Ampere-Maxwell piece of them alone.

[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 percieved 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: FB = 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 my one page site (http://www.quantumnet-string.tk) read the rest (equations etc.). Please read my whole theory and thereby also my atom theory (http://www.physicsforums.com/showthread.php?s=&threadid=8610)

[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: FB = 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 sence 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 sence 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 sence 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