Why is the maxwell's equation not invariant under the galilean transformation?

Question

please explain with simple words/terms... i am just curious and confused.

Answer 1

Because there's a difference between how Maxwell's Equations treat a stationary charge and a moving charge.  A Galilean transformation to a moving frame can cause a current (and therefore a magnetic field) to appear when there was none in a non-moving frame.

In other words, say you're in a frame of reference where there's a charge just sitting 3 meters away from you, not moving.  There will be electric fields, but no magnetic fields.  

Now perform a Galilean transformation so that the charge is traveling past you at 3000000 m/s.  There will be a magnetic field caused by the "current" of this charge moving past.