Effect of motion of a charge in two differenct refrence fremes

[waqarrashid33]

A moving charge produce a megnetic.

But every motion is relative so I want to ask that If a charge is in motion w.r.t one observer but not in motion w.r.t other then what will each observe about the magnetic field of charge?

 

[jambaugh]

This is a good starting point for Special Relativity. Clearly to someone moving along with the charge there will be no magnetic field produced, only an electrostatic field.

To someone moving relative to the charge, (equivalently someone "stationary" when the charge is moving) does see a magnetic field but also sees a different electric field.

The solution to this seeming paradox is that we treat the electric and magnetic components as parts of a unified electromagnetic field. How we break it down into electric and magnetic components is relative to our frame of motion.

Then once you look at Maxwell's equations you can see that they are not invariant under Galilean relativity transformations but are under Lorentz transformations. They are only correct under Einstein's Special Relativity, not Galilean Relativity.

To appreciate this best you need to swim through the mathematics of it.
$$\mathbf{F}' = \Lambda\mathbf{F}\Lambda^T$$
where $F$ is the http://en.wikipedia.org/wiki/Electromagnetic_tensor" and $\Lambda$ is the boost matrix transforming to the new frame of motion.

This is the easiest way (once you have the math and physics tools) to determine the magnetic field of a moving charge. First express the electrostatic field in the charges frame and then Lorentz transform back to the original frame.