Magnetic or Electric Field or Electromagnetic Field?

curiousphoton

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?

DaleSpam

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.

curiousphoton

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?

DaleSpam

Does it matter? As long as you can correctly calculate the force, that is all that the particle experiences.

dgOnPhys

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 wikipedia.

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.

curiousphoton

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?

DaleSpam

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?

Meir Achuz

"The charged particle must experience the same force though in all RF's"
That is not correct. A Lorentz transformation changes the force.

dgOnPhys

I think this is a second order effect we are looking at the low velocity limit (first order approximation) here, right?

curiousphoton

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.

curiousphoton

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...

DaleSpam

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.

Meir Achuz

Can you name that book and give the exact quote?

bcrowell

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.
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.)

curiousphoton

'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.

bcrowell

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.

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.

curiousphoton

Glad you have the book as well. Now I may get more in depth with my questions and they should be easier to follow.

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...