Talk:Electromagnetic field
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Template:Oldpeerreview Skip down to Peer Review: Fluid analogy
E-M Puzzle
Let's say a charged particle moves from point A to point B. It was initially at rest at A, then it suddenly accelerates, moves to B, then decelerates suddenly to stop at B. The electric field around the charge has to change to become centered at its new position. But it cannot change instantaneously throughout all of space because doing so would send information at a speed which is faster than light. So an electromagnetic wave is emitted which has the effect, after it dissipates, of recentering the electric field.
Now, if a charge is moving inertially at a given velocity and then suddenly accelerates to a new velocity but then stays moving inertially at that given velocity, then an electromagnetic wave is transmitted. This is called bremsstrahlung. This is what happens to electrons encountering the ionosphere: they decelerate and produce polar auroras.
If an charged particle is at rest, then it is surrounded by an electrostatic field which is symmetric in every direction. But what if the charge is moving inertially at a constant velocity? Then from its own frame of reference, it is surrounded by an electric field which is static, the same in every direction, without the presence of any magnetic field. But seen from a different frame of reference, the charge is moving, and the electric field has to move along with it, and this is where the problem sets in. If the charge moves along the x-axis, then let's say it moves from x0 towards the "right" to x1 during a unit of time. Point x2 lies directly in the particle's path. The electric field will point, say, away from the proton, and during the unit of time its magnitude will increase. This increase of the electric field at point x2 will cause a circular magnetic field line to be induced, which can be thought of as the rotation of a "magnetic fluid", and the "angular momentum" vector of this rotation points in the direction of the proton's velocity. Then, say there is a point x-1 behind the moving proton. It has an electric field vector pointing in the negative direction, and in one unit of time its magnitude decreases. This means that the electric field vector at point x-1 has increased in the positive direction, thereby inducing -- again -- a circular rotation of the magnetic fluid around it, such that the angular momentum vector of the rotation points in the direction of the proton's velocity.
Therefore the proton, when moving at constant velocity, is surrounded not only by a spherically-symmetric electric field which moves along with it, but also by a cylindrically-symmetric magnetic field whose axis of symmetry parallel to the velocity vector of the proton. Both of these fields decrease in magnitude inversely with the square of the distance. But what does this imply? At any point not directly in the proton's path, there is going to be a magnetic field vector which is perpendicular to the electric field vector. This means that there is going to be a Poynting vector at that point in space.
Points which lie on a transversal plane (perpendicular to the velocity) which includes the charge itself, will have Poynting vectors parallel to the velocity vector, and pointing in the same direction: forwards. Points on transversal planes which are in front of the charge will have Poynting vectors which will also be pointing not only forwards but also inwards towards the path of the charge. Points behing the charge will have Poynting vectors which point not only forwards but also away from the charge's path.
Poynting vectors are associated with electromagnetic waves: they indicate the direction of propagation and the power (rate of energy movement). A proton moving with constant velocity would have Poynting vectors which point in directions tangent to concentric spheres whose centers are the proton. These spheres move along with the proton. These Poynting vectors also all belong to planes which pass through the proton's path. The magnitudes of these Poynting vectors would vary as the fourth power of distance (?). What all these vectors do is to move energy in the direction of the proton. The electric field surrounding a static charge stores energy: this energy is proportional to the magnitude of the electric field vectors. When a charge moves at constant speed, the electric field around it has to move along, somehow, to keep up with its source. This implies a movement of electric energy, and the speed of this movement is power: hence the Poynting vectors.
But if these Poynting vectors describe E-M waves then these must be very unorthodox E-M waves, because they appear to move on the surfaces of spheres, starting all from a single point behind the charge and converging all again at a single antipodal point in front of the charge. Besides, the E and M fields moving along with the particle do not appear to oscillate at all, as would be expected of E-M waves.
Then, what happens if like charges are strung along a line which extends infinitely. If these charges move along their line, then they collectively form a current, even though the charge density remains constant. The constant charge density extending in an infinite line implies a cylindrically-symmetric electric field centered around the line, but the moving charges also imply a cylindrically-symmetric magnetic field. The magnetic field lines are circles whose centers are points on the line of the current. This can be seen to be a consolidation of the one-particle case, but is now equivalent to Ampère's law. Now the Poynting vectors are all parallel to the direction of the current, no matter where they are located in space. This would appear to imply that there are E-M waves moving parallel to the current; but then again, there are no oscillations of the E-M field. Perhaps these E-M waves are "degenerate", or "frozen". By the way, this is an example of a magnetostatic field. --AugPi 10:12, 3 Apr 2004 (UTC)
Peer Review: Fluid analogy
It is nice to see a fresh treatment of a well-known subject. To balance this point of view, the two-fluid analogy should also treat the relationship of the two fluids to each other; we should see how B turns into E and vice versa, in an eternal harmonic motion. The fluid analogy, in fairness to Maxwell's equations, should encompass this.
LePage had a nice model as well. It is not fluids, but the encyclopedia, if it exposes the fluid model, needs to set LePage's viewpoint out as well, for balance.
Also, Faraday's contribution, that the fluids were somehow viscous or rubbery and hence exerted force on the charges.
Also, what about the freeway analogy, which uses the irrotational nature of Maxwell's equations: ie the travel of cars on a freeway obeys Maxwell's equations as well! (covariant motion)
Also, what about Purcell's viewpoint that an electromagnetic field is 'something that crackles'. 169.207.89.249 19:37, 3 Jan 2004 (UTC)
It seems clear that as a front of electrical fluid propogated away from a positive source charge, its velocity of propogation would decrease, which in turn would induce a magnetic field. Is this correct? As someone who doesn't understand EM concepts very well, I think the entry needs to explore in more depth the implications of the fluid analogy.
- The velocity of the moving "particle" of fluid, <math> {d\mathbf{v} \over dt} <math> would decrease indeed, but the velocity field itself would remain constant:
- <math> {\partial \mathbf{v} \over \partial t} = 0 <math>
- The velocity field changes when the particle moves, and when this happens, accelerating electric fluids induce movement of the magnetic fluid, and vice versa, so an electromagnetic wave is propagated. The net effect of this EM wave is to change the velocity field throughout all of space so that it is centered at the new position of the charge. (Imagine changing the position of a Persian rug by lifting one side of it up, then slamming it back down: a wave propagates through the rug, and by the time it reaches the other end, the rug has changed position slightly.) --AugPi 04:28, 24 Mar 2004 (UTC)
The fluid analogy does not work in this sense: that objects immersed in a moving fluid (e.g. a river) tend to be pushed by that fluid in such a way that the velocity of the object aligns with the velocity of the fluid. Once the velocities are aligned, the fluid's motion should vanish from the object's point of view.
However, the force of an electric field on a charged particle is <math> \mathbf{F} = q \mathbf{E} <math>, and this force is independent of the velocity of the particle, which means that the particle will accelerate continually in the direction of the field. If the field is the velocity field of a fluid then the fluid would be causing the object to accelerate continually in the direction of the fluid's motion, to the point that the object's speed becomes way larger than the fluid it is immersed in. This is paradoxical.
From the continually accelerating object's point of view, if its speed has already surpassed the speed of the fluid, then the fluid is moving backwards, so the field should be pointing in the direction opposite to the direction in which the object keeps accelerating. This means that that the object should stop accelerating and begin decelerating, until its speed aligns with the speed of the electric fluid.
An alternative interpretation would be that the field is not actually a velocity field, but a density field of photonic fluid, which is constantly moving at the same speed: the speed of light, independent of the speed of the observer (the charged object). Photonic fluid never changes speed but can change net direction and the intensity of its net movement in that direction. This interpretation would have to be verified by someone who knows QED. --AugPi 02:48, 24 Mar 2004 (UTC).
I just noticed this page listed on the "Peer Review" page, and thought I might add some comments. All these of course, are to be understood as prefixed with "IMHO". The article seems to have a lot of discussion on the fluid analogy and other analogies, so my comments are regarding this aspect.
- The article currently has lots of analogies for the electromagnetic field, but very little discussion of what actually the electromagnetic field is. While analogies are useful upto a point, there is always the risk of getting too excited about them and forgetting to describe something for what it is, rather than what it is similar to.
- As to writing about "what the electromagnetic field really is", the best description, and in a sense the only honest one, is in terms of the field equations. Everything else, analogies, explanations etc. are only attempts to get a 'feel' for these equations. Therefore, a suggestion : the article currently is extremely verbose - it might help if one came up with a leaner, more equation-filled version. The example I have in mind is Maxwell's equations which IMO is now a very decent article.
- Further about analogies : analogies to fluids etc. make sense only when the equations for fluid flow and for the EM field are the same. This happens most transparently in the following cases
- In the continuity equation for the electric charge density, where the charge density in EM and the mass density of a source-less fluid are analogous
- In the divergence equation for the magnetic field, where the magnetic field and the velocity field of an incompressible fluid are analogous.
- Cooking up analogies for the other Maxwell equations seems to lead to some unnecessary obfuscation; and while I am sure it can be described in terms of the interaction of two fluid velocity fields ("electric" & "magnetic" fields), most people who will read the article will not be experts on the fluid dynamics of two (quite weirdly) interacting fluids.
- Regarding the "density field of photonic fluid" : the electric field is not a photon density -- the correct field is more like <math> \ n(\omega) = \frac{1}{2} \frac{\epsilon E(\omega) E^*(\omega)}{\hbar \omega} <math>.
To summarize : There is no point pushing the fluid analogy this far - it seems to be hiding more relevant ideas.
[[User:AmarChandra|Amar | Talk]] 17:18, Jun 30, 2004 (UTC)
I think the fluid analogy in this article hurts more than helps. Most people have a strong intuitive sense of how a fluid should behave, and EM fields do not behave like fluids. They behave like force fields. The article currently relies so heavily on the fluid analogy that I think some people will be confused into thinking that there actually is a ethereal fluid of some kind that makes these processes work, which is not true at all (as far as we know).
I think a better approach would be to help people form an intuition about what a force field (vector field) is. This article is crying out for diagrams; two or three pictures would greatly enhance any verbal explanation. I will try to contribute more specific ideas later as time permits. -- Beland 04:04, 4 Jul 2004 (UTC)
Some comments:
- I agree that there is too much emphasis on the analogy compared to what EM field is in the current version of the article.
- I wouldn't mind having a shorter article on EM field, with links to other well established articles
- I would suggest to create a section "Simple analogies to understand the EM field". It would introduce the subject, then list the various analogies that have been used. Each one would have its own article. This way, the balance between what EM field is, and what it looks like would be more adequate, and there would be plenty of room to describe the analogies.
- I would suggest to introduce the subject by saying that analogies have been important in the history and development of electromagnetism. As an example, the first model of EM was the "tube of force" of Faraday, which did not have any mathematical underpinnings. Maxwell was later very interested in this analogy, which helped him develop his equations. (source: The strange story of the quantum, Banesh Hoffmann, page 10)
Hope it helps... Pcarbonn 20:13, 13 Jul 2004 (UTC)