# Deviation of compass in another frame

1. Jun 5, 2014

Consider an inertial frame where an electric current is flowing in upward direction, a magnetic field is created and its direction is determined by the right hand rule.
In the frame of reference of the electric charges which they are at rest, how can the observer in that frame explains the magnetic field that developed in another frame moving relative to his frame? For example, how can he explain a deviation of a compass in the other frame that is moving relative to him?

2. Jun 5, 2014

### cosmosmike

If the compass is moving past the electrical charges, the compass sees a current in his frame.

3. Jun 5, 2014

yes I know. My question, how the observer riding over one of the charge can explain the deviation of the compass?

4. Jun 5, 2014

### mattt

The electromagnetic field tensor is the same in both frames (but its coordinates are different, in general, in two different frames).

5. Jun 5, 2014

### Staff: Mentor

Here is a good reference for how electromagnetic fields transform between inertial frames.
http://farside.ph.utexas.edu/teaching/em/lectures/node123.html

Note, if your wire is uncharged then there is no frame where there is no current. If the electrons are at rest in a frame then the protons are moving. Either way there is a current and therefore a magnetic field.

6. Jun 6, 2014

so there is a current seen by an observer moving with electrons because of the protons moving in the opposite direction.

How if there is no protons, in other words, how if an electrons gun is emitting electrons, will be still any magnetic field in the frame where electrons are moving? and how the observer in the rest to the moving electrons can explain the magnetic field B?

Now back to the current again. I read the link of transformation equation and I attached a PDF file of 1 page., so please go through it.

By the way, how to attach a picture directly in the text instead of thumbnail.

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7. Jun 6, 2014

### Drakkith

Staff Emeritus
A frame in which the electrons are moving has a magnetic field precisely because the electrons are moving. A frame co-moving with the electrons, IE a frame where they are stationary, sees no magnetic field, and instead sees an electric charge from all those electrons.

8. Jun 6, 2014

Fine, so how the observer comoving with electrons explain the deviation of a compass in another frame which is moving relative to him?

9. Jun 6, 2014

### cosmosmike

Does anyone know where I can find a derivation of the magnetic field of a moving point charge from Ampere's Law? (not the Biot Savart law, but directly from Ampere's law).

10. Jun 6, 2014

### WannabeNewton

Drakkith already answered this. In that frame the electrons are moving and thus produce a magnetic field so a compass at rest in that frame will be deflected. A compass at rest in the comoving electron frame will not be deflected because there is only an electric field in that case.

You need all of Maxwell's equations to get the magnetic field of a moving point charge because this is not a stationary charge configuration. Ampere's law by itself is not enough.

If the charge is moving at uniform velocity in some inertial frame then there is a much easier way to get its magnetic field in this frame: just take the Coloumb field in the charge's rest frame and Lorentz boost to the original frame, thus Lorentz transforming the Coulomb field and obtaining the electric and magnetic fields of the uniformly moving charge in the original frame.

11. Jun 6, 2014

Is the physical phenomena explained only in the frame where it happens?
I know that the explanation is sound in the frame of the compass. I am asking about the way an observer riding on the current can explain it?

for example, in the "moving magnet and conductor problem", the same physical phenomena could be explained in both the conductor frame as well as the magnet frame. http://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem

12. Jun 6, 2014

### WannabeNewton

Yes certainly. What happens to a magnetic dipole moving through a static electric field?

13. Jun 6, 2014

14. Jun 6, 2014

### Staff: Mentor

Yes.

This is a physically different scenario from the first. I would strongly recommend staying with one scenario until you understand that one scenario before jumping to another. You have already gotten some good replies, but I think that it is a mistake to pursue it.

Equation 1 is incorrect in general. In general r≠r' and I≠I', and therefore B≠B' despite the fact that the EM field follows Maxwell's equations in both frames.

Equation 2 is correct for this scenario. E=0 because the wire is uncharged in its rest frame in this scenario.

Last edited: Jun 6, 2014
15. Jun 6, 2014

### Staff: Mentor

There is no such thing as "the frame where it happened". Every physical phenomenon happens in every frame. Different frames are simply different ways to describe the same "happenings". The explanations may be different, but the phenomena are the same.

It is unclear what scenario you are asking about. I really wish you had just stuck with one.

All classical EM scenarios in all frames are explained by Maxwell's equations. The fields can be transformed according to the link I sent, and nearby you can also find links to see how the sources transform. And space and time transform according to the Lorentz transform.

16. Jun 7, 2014

That is fine. So how the observer riding on the current can explain the force acting on the compass which is moving relative to him? What formula described the force affecting a moving magnet dipole n the field of a stationary static electric field?

17. Jun 7, 2014

I understand that r is the perpendicular distance from the wire. So it should not be affected by length contraction.

I for an observer where the compass is at rest depends on Q and t. for an observer co-moving with the charge, he still considers the current moving in the same direction with the same velocity. So the same calculation is still hold for him as in the first observer.

18. Jun 7, 2014

I posted a different post under the name "time to train stop" in the SR and GR forum. The discussion went fine until the last page where I still did not find a reply on a thought experiment I proposed. In that one, the decrease in the length of the train when it stops relative to the train observer may cause different physical phenomena as compared with another observer in the platform. So would you please have a look at it and your kind reply is appreciated.

19. Jun 7, 2014

### WannabeNewton

20. Jun 7, 2014