# 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 shouldn't 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... I am in high school ok

Thanks for any help

Kartik

sridhar_n
Hi

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

kartiksg
I still don't get how to apply v in the formula. Relative to what? How do I sense the movement relative to a field? Also, according to 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 shouldn't 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... I am not sure what its magnitude will be as I don't 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 I am 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

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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:

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,

&part;Fab/&part;xa = 4&pi; jb

&part;Fbc/&part;xa + &part;Fca/&part;xb + &part;Fab/&part;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 &epsilon;0's and &mu;0'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 = &part;Ab/&part;xa - &part;Aa/&part;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.

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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

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

Homework Helper
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 [Broken]

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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.

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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... I am 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 .

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 [Broken] 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? ( I am 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 ( all tongue twisted.. ).

Thanks

Kartik

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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 ( 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 &gamma; = 1/&radic;(1-(v/c)2), because there is length contraction by a factor &gamma; along the direction of motion, shrinking the volume and increasing the density.

Also, it was stated in www.modernrelativity.com [Broken] 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 &gamma; implicitly in its definition; if you use invariant mass instead, then that &gamma; 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 [Broken]

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

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Homework Helper
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 a lot like a matrix, called a second rank 4-D tensor. A simple vector just won't do anymore. Then, you have something a lot 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 &gamma; 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?

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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 into 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.

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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 into 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 referring 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 sense 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 referring 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 sense 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 traveling 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 sense 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).

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Fairfield
Zooby:

Did you catch that it is acceleration relative to an EMF that produces an electromagnetic wave, not Newtonian spatial 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.

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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).

Homework Helper
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,

Ambitwistor
Originally posted by turin

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.

Homework Helper
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.

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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.