Is magnetic field a frame dependent quantity?

[ank160]

A moving charge constitutes current, which in turn produce magnetic field around it. So does that mean if the observer is also moving with charge, then it will not experience ne magnetic field?
And if the same observer is carrying a permanent magnet, then it will not show ne motion to align itself in accord with magnetic field. But if the same magnet is palced in stationary frame then it will align itself as per magnetic field?

Plz help

 

[The_Duck]

These are the questions that lead to special relativity! Indeed, if you are in a frame where some charge is not moving, then that charge produces no magnetic field, only an electric field. Observers moving relative to each other observe different electric and magnetic fields. Of course, they must agree on how these fields will affect the motions of test charges dropped into them. So there must be some close relationship between the fields in one frame and the fields in another to allow different observers to predict the same motions for charged particles. If you accept Maxwell's equations then this requirement implies "strange" effects like length contraction and time dilation.

Alternatively, you can go the derive Maxwell's equations from Coulomb's law and special relativity. In this route you see that magnetism must appear given only Coulomb's law for stationary charges along with the principles of special relativity.

You can check out these Wikipedia pages:

http://en.wikipedia.org/wiki/Relativistic_electromagnetism
http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity

Perhaps you can see the same concerns in the first paragraph of Einstein's 1905 paper introducing special relativity:

It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing
a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.

 

[Dale]

A moving charge constitutes current, which in turn produce magnetic field around it. So does that mean if the observer is also moving with charge, then it will not experience ne magnetic field?
And if the same observer is carrying a permanent magnet, then it will not show ne motion to align itself in accord with magnetic field. But if the same magnet is palced in stationary frame then it will align itself as per magnetic field?

Yes, you seem to understand correctly. As The_Duck mentioned, this is what lead to special relativity.

 

[harrylin]

Right. Note however that you can't make the magnetic field of a common electromagnet (an electrically neutral coil) disappear by means of a Lorentz transformation.

 

[Antiphon]

However, you can always find an accelerated frame in which it does vanish (for the common electromagnet.)