Magnetic or Electric Field or Electromagnetic Field?

In summary: where they can unambiguously say that the charged particle traveled through a magnetic field or an electric field?
  • #1
curiousphoton
117
2
Bob Reference Frame:
A charged particle moves through a uniform magnetic field with velocity V. No electric field is present and gravitational forces may be neglected. The charge thus experiences a force due to this magnetic field equal to F = qV x B. B is the strength of the magnetic field.

SALLY RF:
Sally runs at velocity V (V remember is the velocity of the charged particle as well). Because the charged particle is at rest in Sally's RF, there is no magnetic force present. The charged particle must experience the same force though in all RF's so the force calculated in Bob's RF (due to the magetic field in Bob's RF) must be somewhere else in Sally's RF. It is found that in Sally's RF, there is an electric field equal to F' = qE'. F must equal F' so qE' = qV x B.

CONCLUSION / INQUIRY

The charged particle, according to Bob, travels through a magnetic field. The same charged particle, according to Sally, travels through an electric field.

Question: Is Bob incorrect if he said the charged particle traveled through a magnetic field only? Is Sally incorrect if she said the charged particle traveled through an electric field only? Am I incorrect if I say the particle traveled through an electromagnetic field only?
 
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  • #2
You should read the second part of Einstein's famous "On the electrodynamics of moving bodies". It covers the transformations of electric fields into magnetic fields and vice versa. As you have correctly identified, the electric and magnetic field vectors are frame dependent components of the electromagnetic field tensor.
 
  • #3
DaleSpam said:
You should read the second part of Einstein's famous "On the electrodynamics of moving bodies". It covers the transformations of electric fields into magnetic fields and vice versa. As you have correctly identified, the electric and magnetic field vectors are frame dependent components of the electromagnetic field tensor.

Thanks for the resource. I will see into reading it. My physics textbook covers transformations of electric fields into magnetic fields. I guess I'm still stuck on first base though as I don't quite understand which exists for a given problem.

As in my example, I can transform magnetic and electric forces between the two RF's (Bob and Sally). I'm stuck on whether the charged particle actually experiences a magnetic field or an electric field or an electromagnetic field?
 
  • #4
Does it matter? As long as you can correctly calculate the force, that is all that the particle experiences.
 
  • #5
curiousphoton said:
...

CONCLUSION / INQUIRY

The charged particle, according to Bob, travels through a magnetic field. The same charged particle, according to Sally, travels through an electric field.

Question: Is Bob incorrect if he said the charged particle traveled through a magnetic field only? Is Sally incorrect if she said the charged particle traveled through an electric field only? Am I incorrect if I say the particle traveled through an electromagnetic field only?

Your conclusion seem to suggest that Sally is not seeing any magnetic field, but this is not true. The magnetic field will still be the same in Sally's RF but the particle being at rest won't experience any force from it. You can refer to http://en.wikipedia.org/wiki/Classi...les-Bernoulli_equation_for_fields_and_forces".

The charged particle, according to Bob, travels through a magnetic field. The same charged particle, according to Sally, is at rest in a static electric field and in a static magnetic field.

Since all fields are static in both RFs usually you do not talk of electromagnetic field but strictly speaking it would be correct. There are just no electromagnetic waves, field energy is not propagating.
 
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  • #6
DaleSpam said:
Does it matter? As long as you can correctly calculate the force, that is all that the particle experiences.

I think it matters and think it is very interesting. If someone walked up to Bob and said "You measured the force on the charge particle to be x. Did the particle travel through a magnetic field or electric field?" Bob replies "Magnetic of course".

Next, Sally is asked the same question: "You measured the force on the charge particle to be x. Did the particle travel through a magnetic field or electric field?" Sally replies "Electric of course".

I find this to be an interesting paradox. Both Bob and Sally made two different observations of the same event and both are observations are correct.

I'm wondering: did the charged particle really travel through a magnetic field or did the charged particle really travel through an electric field?
 
  • #7
curiousphoton said:
I find this to be an interesting paradox.
Strictly speaking, as long as they both agree on the measured result of any experiment then there is no paradox.


curiousphoton said:
I'm wondering: did the charged particle really travel through a magnetic field or did the charged particle really travel through an electric field?
Can you give me an operational definition of what you mean by the word "really"? In other words, what physics experiment can Bob and Sally perform to determine which "really" happened in your meaning of the word?
 
  • #8
"The charged particle must experience the same force though in all RF's"
That is not correct. A Lorentz transformation changes the force.
 
  • #9
Meir Achuz said:
"The charged particle must experience the same force though in all RF's"
That is not correct. A Lorentz transformation changes the force.
I think this is a second order effect we are looking at the low velocity limit (first order approximation) here, right?
 
  • #10
Meir Achuz said:
"The charged particle must experience the same force though in all RF's"
That is not correct. A Lorentz transformation changes the force.

The physics textbook I was reading stated that the charged particle experienced the same force regardless of the RF as long as the RF was intertial.
 
  • #11
DaleSpam said:
Strictly speaking, as long as they both agree on the measured result of any experiment then there is no paradox.


Can you give me an operational definition of what you mean by the word "really"? In other words, what physics experiment can Bob and Sally perform to determine which "really" happened in your meaning of the word?

Good point. Well if Sally stopped moving with the charged particle and came to rest in Bob's RF, then they would both agree the charged particle was traveling through a magnetic field which supplied the force F. And vice versa...If Bob increased his speed until he reached a constant velocity (equal to Sally's and the charged particle), then Bob and Sally would agree the charged particle was traveling through an electric field which supplied an equal force F.

I'm just interested in the view of the charged particle. Is it traveling through an electric field, magnetic field, or both, or a differnent type of electromagetic field...
 
  • #12
curiousphoton said:
I'm just interested in the view of the charged particle. Is it traveling through an electric field, magnetic field, or both, or a differnent type of electromagetic field...
The particle is at rest wrt Sally, so their reference frame is the same. In the Sally/particle frame there is both an electric and a magnetic field.
 
  • #13
curiousphoton said:
The physics textbook I was reading stated that the charged particle experienced the same force regardless of the RF as long as the RF was intertial.
Can you name that book and give the exact quote?
 
  • #14
One thing that I don't think has been touched on yet is that I think the OP was imagining a field that was purely E in one frame and purely B in another frame. That's not possible, and I think one way to show it is that E2-B2 (in units where c=1) is Lorentz invariant, so it can't flip signs.
curiousphoton said:
The physics textbook I was reading stated that the charged particle experienced the same force regardless of the RF as long as the RF was intertial.
Meir Achuz was right. Either your textbook is oversimplifying or you missed somewhere that they stated they were making a low-velocity approximation. This whole topic is much easier to present in a way that's intelligible to students if you use low-velocity approximations, so that's what most books do. IIRC Purcell avoids approximations, and that's is the only lower-division book I know of that does so. (Purcell is a great book, by the way.)
 
  • #15
Meir Achuz said:
Can you name that book and give the exact quote?

'Physics for scientists and Engineers' - Chapter 34

-Randall D. Knight

I don't have it avaiable to me at the moment but will recite the exact quote soon.
 
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  • #16
curiousphoton said:
'Physics for scientists and Engineers' - Chapter 34

-Randall D. Knight

I don't have it avaiable to me at the moment but will recite the exact quote soon.

I have the book. Section 34.2 says:
Sharon claims that F=0...Now, we may be a bit uncertain about magnetic fields, because they are an abstract concept, but surely there can be no disagreement over forces. After all, the charge is either going to accelerate upward or it isn't, and Bill and Sharon should be able to agree on the outcome.

I can see how you could get the impression from this passage that force is relativistically invariant. The main thing to realize here is that the final sentence can be phrased as a statement about intersections of world-lines, and such statements *are* frame-independent. Sharon's charge Q is going to lift off of the little pedestal on which she's carrying it, and it will accelerate upward and hit a certain point P on the ceiling. The fact that P and Q's world-lines will intersect is frame-independent.

Regarding the forces, things are a little more complicated than Knight is letting on here. Forces are not relativistically invariant, but he isn't going to do relativity until ch. 36, so he doesn't want to get too deeply into that here.
 
  • #17
Glad you have the book as well. Now I may get more in depth with my questions and they should be easier to follow.

bcrowell said:
I have the book. Section 34.2 says:


I can see how you could get the impression from this passage that force is relativistically invariant. The main thing to realize here is that the final sentence can be phrased as a statement about intersections of world-lines, and such statements *are* frame-independent. Sharon's charge Q is going to lift off of the little pedestal on which she's carrying it, and it will accelerate upward and hit a certain point P on the ceiling. The fact that P and Q's world-lines will intersect is frame-independent..

I follow you up to here. I was trying to get more at what makes causes the charge Q to accelerate up to point P in Sharon and Bill's reference frame. In Bill's RF, a magnetic field provided the force which caused the charge Q to accelerate to point P. In Sharon's RF, an electric field provided the force which caused the charge Q to accelerate to point P.

If you read under equation 34.6, Knight states: 'Sharon and Bill may measure different positions and velocities for a particle, but they agree on its acceleration. This agreement is important because acceleration force F = ma is acting on the particle. Similary, the force measured in frame S' is F = ma'. But a' = a, hence F' = F. Experimenters in all interial reference frames agree about the force acting on a particle. This conclusion is key to understanding how different experimenters see electric and magnetic fields.'

Furthermore, if you read under equation 34.8, Knight states: 'Whether a field is seen as "electric" of "magnetic" depends on the motion of the reference frame relative to the sources of the field.'

Taking this information into account (read carefully and assuming the authors statements to be true), am I wrong to say that neither Bill nor Sharon are either wrong or right about whether a magnetic field caused the charge, Q to accelerate to point P or an electric field caused the charge Q to accelerato to point P. It seems they are both right and or wrong...
 
  • #18
Experimenters in all interial reference frames agree about the force acting on a particle.
This statement is false. But then, Knight also states Newton's second law, which is false, and conservation of mass, which is false. All of these things are false relativistically, but he states them as facts in the chapters of the book before he gets to relativity (which is the very last chapter of the book).

Whether a field is seen as "electric" of "magnetic" depends on the motion of the reference frame relative to the sources of the field.
This is true, provided that you don't interpret it to mean that a field that is *purely* electric in one frame can be *purely* magnetic in another -- that would be false.
curiousphoton said:
Taking this information into account (read carefully and assuming the authors statements to be true), am I wrong to say that neither Bill nor Sharon are either wrong or right about whether a magnetic field caused the charge, Q to accelerate to point P or an electric field caused the charge Q to accelerato to point P. It seems they are both right and or wrong...
You've got it. Each person's description is right, in that person's frame.
 
  • #19
curiousphoton said:
'Sharon and Bill may measure different positions and velocities for a particle, but they agree on its acceleration. This agreement is important because acceleration force F = ma is acting on the particle. Similary, the force measured in frame S' is F = ma'. But a' = a, hence F' = F. Experimenters in all interial reference frames agree about the force acting on a particle. This conclusion is key to understanding how different experimenters see electric and magnetic fields.'
bcrowell said:
This statement is false. But then, Knight also states Newton's second law, which is false, and conservation of mass, which is false. All of these things are false relativistically, but he states them as facts in the chapters of the book before he gets to relativity (which is the very last chapter of the book).
They are all false in general, but they are also all correct in the limit v<<c. It is very hard to write a book like this without introducing concepts too early for the student to understand. I don't have that book, does he specifically mention "small v" or any similar caveat?

Relativistically there are things that could be said to make this correct. E.g. "Sharon and Bill may measure different positions and velocities for a particle but they agree on its proper acceleration" and "Experimenters in all inertial reference frames agree about the magnitude of the four-force acting on a particle".
 
  • #20
DaleSpam said:
They are all false in general, but they are also all correct in the limit v<<c. It is very hard to write a book like this without introducing concepts too early for the student to understand. I don't have that book, does he specifically mention "small v" or any similar caveat?

No, he doesn't. It's a couple of chapters before he does relativity, but he's clearly leading up to relativity. There is a section soon after this titled "Almost Relativity."
 
  • #21
Hmm, that's too bad. I believe that you can specify conditions like that without introducing confusion, particularly if you parenthetically refer to the later chapters where you will eventually discuss the general case. Not doing so causes problems.
 
  • #22
bcrowell said:
This statement is false. But then, Knight also states Newton's second law, which is false, and conservation of mass, which is false. All of these things are false relativistically, but he states them as facts in the chapters of the book before he gets to relativity (which is the very last chapter of the book).

So if this statement is false, why is it bolded? Clearly he is trying to make the point that understaing the statement as true is very important (hence the bolding of the text). Sorry just wondering why he would do this.

bcrowell said:
This is true, provided that you don't interpret it to mean that a field that is *purely* electric in one frame can be *purely* magnetic in another -- that would be false.

You've got it. Each person's description is right, in that person's frame.

As for my background, I took 1 1/2 years of physics at my university (Cal Poly, where Knight is a professor), which used this book and covered up through Chapter 33. I graduated last year and in my free time started reading the last 3 chapters. I've read Einstein's 'Relativity' book prior to starting chapters 34-36 so I'm familar somewhat with relativity.
 
  • #23
curiousphoton said:
So if this statement is false, why is it bolded? Clearly he is trying to make the point that understaing the statement as true is very important (hence the bolding of the text). Sorry just wondering why he would do this.

Probably because it's an important point in his argument. I'm sure Newton's second law is highlighted or in bold-face or something as well -- but it's false in relativity.
 
  • #24
You're having the same problem with the idea of "force" and what it means, which I used to have.

There is only one frame in which force is physically meaningful, that being the frame of the particle or Sally, because it can be measured statically and hence independently of its velocity. Using F = dp/dt in this frame and then using the Lorentz transfromations, you can work out the equation of motion in any other frame.

You can define relativistic force in a number of ways, but usually such that F = dp/dt for v = 0. F = d/dt (gamma mv) is commonly used, the Minkowski force being another.

So what does F = d/dt(gamma mv) "really mean"?

Simply that it's just a mathematical expression that packages the acceleration terms in a certain way and does not physically mean "the force on a particle", except for v=0.

Using your example, Sally measures the electric force on the particle, whereas everyone else measures an equation of motion that can be paramaterised using an E and B for that frame.

Does this help?
 
  • #26
I emailed Knight a while back to suggest clarifying this passage. Received an email from him today saying that he was in the process of producing a 3rd edition, and that he would keep this in mind while revising the book.
 
  • #27
bcrowell said:
I emailed Knight a while back to suggest clarifying this passage. Received an email from him today saying that he was in the process of producing a 3rd edition, and that he would keep this in mind while revising the book.

Cool. Thanks for the follow up. It will be interesting to re-read this section in the new 3rd edition.
 

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be observed. It is created by the movement of electric charges, such as electrons, and can be represented by lines of force.

2. How is a magnetic field different from an electric field?

A magnetic field is created by moving electric charges, while an electric field is created by stationary electric charges. Additionally, electric fields act on both positive and negative charges, while magnetic fields only act on moving charges.

3. What is an electromagnetic field?

An electromagnetic field is a combination of both electric and magnetic fields. It is created when an electric current flows through a conductor, producing a magnetic field, and the changing magnetic field induces an electric field.

4. How are magnetic and electric fields used in technology?

Magnetic and electric fields have a wide range of applications in technology. Electric fields are used in electronic devices such as computers and cell phones, while magnetic fields are used in generators, motors, and MRI machines.

5. Can exposure to electromagnetic fields be harmful?

There is ongoing research on the potential health effects of exposure to electromagnetic fields. While high levels of exposure can be harmful, the levels typically found in our daily lives are not considered to be a significant health risk.

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