Drift speed and current in two different inertial frames We have a long, cylindrical wire carrying a constant current $I$ in an inertial frame. At a distance of $R$ from the center of the wire, the magnitude of magnetic field is $μI/2 \pi R$.
What is the magnitude of magnetic field in another inertial frame moving at a certain speed opposite to the direction of electric current? 
Since the observed drift speed of the electrons is now greater, does this mean that the current as observed from this frame is greater? 
If so, what about the magnetic field due to this current? Does this change too?  
In general how do currents vary between different frames of reference?
 A: The magnetic field arises because of relativity. Imagine a frame of reference, $A$ in which a charge Q is at rest. If another charge q is brought close, it will experience an electrostatic force. On another inertial frame of reference $B$ with velocity $v$  with respect to $A$, both the charges are moving. The static charges on $A$ appear as charges and currents. The electrostatic field of $A$ becomes as an electrostatic field of different magnitude and a magnetic field.
magnetism due to a current can be considered to be a relativistic effect.
Permanent magnetism of a bar magnet is not a relativistic effect because of the electron's spin and not orbital motion.
A: Current can be represented as 

$ I  = n e v_d A$
  Here $n$ is no of electron per unit volume, $e$is charge of electron, $A$ is area of cross section from where they are flowing and $v_d$ is drift speed.

In a general case, we define $ v_d = eE\tau /m_e $, here $E$ is field electrons move in, $m_e$ is mass of electron and $\tau$ is relaxation time
But when you see from a frame moving with velocity $v$, the electrons seem to move with net velocity $v_d + v$. In this case the net current would be given as :

$I = n e (v_d + v) A$

Since the current changes, so does the magnetic field.
The above equation can also be written as:

$ I = n e A v + n e v_d A$
      This is like $ y = mx + c$

Therefore current varies linearly with the speed of observer.
