# Magnetic field of a moving charged particle

1. Oct 25, 2013

### arul_k

A moving charged particle produces a magnetic field around it, thus a stationary observer would notice a moving electric and magnetic field.

Does this moving magnetic field (as seen by the stationary observer) in turn produce another electric field?

2. Oct 25, 2013

### Staff: Mentor

I think it's more accurate to look at it this way:

The particle has an EM field around it that is purely electrical as seen by an observer who is stationary with respect to the particle, and partly magnetic and partly electrical as seen by an observer in motion with respect to the particle. I don't think either of fields "create" a new field.

Someone correct me if I'm wrong.

3. Oct 25, 2013

### Crazymechanic

You can't even create an electric field , it's already there , every charged particle has it as a fundamental entity.
All we do is play around with it and watch what happens , like two stationary particles one is charged and the other is not, it is the " observer" particle.
Now the observer particle sees an electric field from the charged particle , a stationary electric field with a fixed value at any given distance, which decreases in strength with distance.

Now if you start to move the charged particle , the observer particle sees the electric field lines from the charged particle to start to deflect so to say.
Now it sees a magnetic field.
Actually there is no magnetic field , there is only electric one , the magnetic field arises around the movement of charged particles.Or as distorted electric field lines due to different frames of reference which involves SR.
But if nothing would move and you could somehow keep the charged particles stationary there would be no magnetic field just electric one, as long as something moves doesn't matter if the observer or the charged particle , the one sees a magnetic field while the other sees an electric one.

4. Oct 25, 2013

### Staff: Mentor

I'd be careful in saying there is no magnetic field. Think about the magnetic field of particles due to their intrinsic spin. There is no frame of reference where this magnetic field does not exist. At least not to my knowledge.

5. Oct 25, 2013

### Crazymechanic

yes particles have this phenomenon due to spin but then again what is spin... movement.
Well ofcourse it's a fundamental phenomenon of matter , atleast from a classical point of view.Still without that movement you would just have an electric field possessing charged particle.
Even though a complicated matter , maybe better left out of the picture of this thread.

6. Oct 25, 2013

### WannabeNewton

This is incorrect. The electric field is not more fundamental than the magnetic field. In fact what is true is that there is a single (covariant) electromagnetic field.

Arul, if the magnetic field is time varying in the frame of the stationary observer then it will have assocaited with it a locally circulating electric field as per Faraday's law $\nabla \times E = -\frac{1}{c}\partial_t B$ in said frame.

7. Oct 25, 2013

### arul_k

Thanks Drakkith and Crazymechanic for your answers, but my question pertains to the magnetic field that is observed by the stationary observer.
For a moving charged particle a stationary observer will also observe a moving magnetic field, does this moving magnetic field give rise to an electric field apart from the particles original electric field.

8. Oct 25, 2013

### arul_k

Thanks WanabeNewton for your answer. If I understand correctly this locally circulating electric field is inependent of the charged particles electric field. If so, how would this locally circulating field interact with the charged particles original field?

9. Oct 25, 2013

### Crazymechanic

It's not independent as the magnetic field the observer sees is caused by the traveling charged particle which has a certain charge and velocity as compared to the stationary observer , in other words charged particles are not independent of the respective fields nor are the fields free from the particles.

I'm sure wannabeNewton will elaborate on this whole thing.

10. Oct 26, 2013

### arul_k

I know the field is not independent of the charged particle, what I asked is if the new circulating field is independent of the original electrical field

11. Oct 26, 2013

### HallsofIvy

Staff Emeritus
A changing electric field produces a magnetic field and a changing magnetic field produces an electric field.

A charged particle moving at a constant speed produces a constant magnetic field. That constant magnetic field does NOT produce another electric field. If the charged particle were accelerating then it would produce a changing magnetic field which would produce another elecftric field. In particular, a periodically moving charged particle (as in harmonic motion) produces an electro-magnetic field.

12. Oct 26, 2013

### Staff: Mentor

The complete field from an arbitrarily moving charged particle is given by the Lienard Wiechert potential:
http://en.wikipedia.org/wiki/Liénard–Wiechert_potential

13. Oct 26, 2013

### arul_k

A bar magnet moving with uniform velocity would produce an electric field around it, there is no accleration or changing magnetic field here, only relative motion of the magnetic field.

Similarly one one expect the moving magnetic field around the charged particle to produce an electric field.

DaleSpam, I read the wiki article, but could not find any direct reference to my question.

14. Oct 26, 2013

### mikeph

The fields wouldn't interact. The charge itself creates a divergent part of the field and the time derivative of B will create a rotational part of the field. These two parts are generated separately, they should just add and produce an overall diverging and rotating field.

15. Oct 26, 2013

### WannabeNewton

mikeph already stated what I was going to state (sorry for the late reply) so at this point I just want to bring to note a phrase you keep using: " moving magnetic field". Perhaps you already know this but you keep using this phrase so let me just point out that the magnetic field does not move.

16. Oct 26, 2013

### Staff: Mentor

You can use the formulas I provided to calculate the fields. Then you can directly see if the "moving fields" generate any electric fields.

17. Oct 26, 2013

### dauto

If I understand the question correctly, the OP seems to believe that the electric field produced by the varying magnetic field (as per Faraday law) is in addition to the electric field produced by the moving particle. That's incorrect. They are one and the same. The fields that appear in Faraday's equation are the total fields. There is nothing left out that must be added to it. How many different ways can I say that?

18. Oct 27, 2013

### arul_k

What I mean by "moving magnetic field" is the "magnetic field associated with a charged particle moving with uniform velocity wrt a stationary observer", it was just easier to use the term moving magnetic field.

19. Oct 27, 2013

### arul_k

Quite honestly, DaleSpam, the math is above me, I haven't studied advanced math. I would appreaciate it if you could tell me if the moving fields generate any electric fields.

20. Oct 27, 2013