Electric & Magnetic Fields
So many posts, and such spread out & confused issues. So let me pose the obvious question to Farsight, maybe already answered somewhere buried in some thread, but clear explicit statements seem hard to come by: Do you claim that the electric field is not in fact a "field" at all, and that it is wrong to call it a "field", given some appropriately rigorous definition for a "field"?
I asked because the issue of what
Farsight really means seems to be clouded by
Farsight's own words, for example …
On 19 June ...
I said the electromagnetic field is a field, but that the electric field and the magnetic field aren't.
On 21 June ...
Yes it can be useful to talk of electric fields and magnetic fields separately, ...
The first is certainly a clear enough claim that the electric and magnetic fields are not in fact fields. But then only two days later, he implies that, OK, they are fields and it may even be useful to talk about them, but it's really the electromagnetic field we should always be talking about. I am not going to worry about mind-reading at the moment, and just look at the two points, as I see them.
First the easy one, the idea that electric & magnetic fields are useful, but it's really the electromagnetic field we should be talking about. Well, really, everybody who ever studied physics (and remained awake in class at least most of the time) knows very well that Maxwell took electric and magnetic and created from them the unified electromagnetism. And physicists certainly do talk about the unified electromagnetic field whenever it is appropriate, and likewise about electric and magnetic fields when they are appropriate; as
Farsight suggests, it is useful, but apparently more useful than he thinks. Allow me at this point to shamelessly quote from the collected literature of physics:
"The force of the first type, per unit charge, is called the electric field intensity; we denote it by E. So, by definition,
E = -(1/c)(∂A/∂t) - grad Φ
The factor of v/c in the force of the second type, per unit charge, is called the magnetic field intensity. We designate it by H. So, by definition,
H = curl A
[highlight]If, in an electromagnetic field, E ≠ 0 but H = 0, then we speak of an electric field; if E = 0 but H ≠ 0, then the field is said to be magnetic. In general, the electromagnetic field is a superposition of electric and magnetic fields.[/highlight]"
The Classical Theory of Fields (4th revised English edition), Landau & Lifshitz , 1975 (reprinted with corrections 2005). Chapter 3, "Charges in Electromagnetic Fields" (pages 50-51, italics from the original; the highlight is mine).
Two for the price of one. Clearly, if electro = nothing but magneto = something, then we don't have electromagnetism, we just have magnetism, and vice-versa. But we also see that the electric
field and the magnetic
field combine into the electromagnetic
field; there is nothing about the physics of fields which prevents one field from being a superposition of multiple other fields. In this case the two, electric & magnetic, combine into the third, electromagnetic. The idea that electric fields and magnetic fields are not fields, as explicitly pointed out at least once by
Farsight, does not seem to pass the test of physics (as most of you of course already know).
Now, about that "what is a field" thing. Since my own brief & casual foray into trying to find a reasonably rigorous definition for a "field" was unsatisfactory, let me try again, after following the advice to "do my own research".
A field is a function that associates one or more numbers with each point in space. Two types of field are distinguished: scalar and vector, depending on whether the field function assigns either a scalar or a vector value to each spatial location. The gravitational potential of the Earth is a scalar field, and the force of gravity is a vector field (all forces point towards the center of the Earth).
The Six Core Theories of Modern Physics, Charles F. Stevens, MIT Press 1995 (sixth printing, 2002), page 2 (emphasis from the original).
I was rather hoping for something that combined brevity with rigor; while this seems to award the former more than the latter, it still seems both rigorous enough & correct enough for our work. It should be, as my old instructors liked to say, "obvious by inspection" that both the electric
field and the magnetic
field meet the criteria established here for a
field (the definition does not deal with the technicality of vector vs pseudovector, in describing a vector field, but if one allows a casual use of the word "vector" it does the job).
But maybe we can do better ...
"The interaction of particles can be described with the help of the concept of a field of force. Namely, instead of saying that one particle interacts with another, we may say that the particle creates a field around itself; a certain force then acts on every other particle located in this field. In classical mechanics, the field is merely a mode of description of the physical phenomenon - the interaction of the particles. In the theory of relativity, because of the finite velocity of propagation of interactions, the situation is changed fundamentally. The forces acting on a particle at a given moment are not determined by the position at that same moment. A change in the position of one of the particles influences other particles only after the lapse of a certain time interval. This means that the field itself acquires physical reality. We cannot speak of a direct interaction of particles located at a distance from one another. Interactions can occur at any one moment only between neighboring points in space (contact interaction). Therefore we must speak of the interaction of the one particle with the field of the second particle."
The Classical Theory of Fields (4th revised English edition), Landau & Lifshitz , 1975 (reprinted with corrections 2005). This is the first paragraph of chapter 3 (page 46), "Charges in Electromagnetic Fields" (emphasis from the original).
I present that, so as to address this ...
Neither of those particles ever had an electric field as opposed to an electromagnetic field.
This strikes me as an issue of semantics, not physics; indeed, in any sense of physics, it's just absurd. As an exercise in semantics, it might be forgiven. Given the various definitions shown above, an
electric field is an
electromagnetic field with the magnetic component equal to zero. Choose either one, and it will work just fine. Then we can splutter on as long as we like that it must be an electromagnetic field, not an electric field, and have language available whereby to feel better about ourselves. But the physicist will ignore the linguistic mumbo-jumbo and simply treat the particle as having an electric field and be done with it.
Some windmills are useless tilting targets, and this is one. Of course the electric
field and the magnetic
field are real-live, honest to gosh
fields, and all the linguistic tricks and clever exegesis of physics texts will not change that. Everything in physics is what the equations say it is, and if the equation says "
field", then by golly it's a
field, like it or not. And that is exactly what the equations say.