jcc:
if electrons move that slow, why is current fast like light speed?
Suppose you turn on the ceiling light switch in your room. The light that it activates is probably several metres away from the switch, but it turns on practically instantly when you flick the switch. But if you calculate how long it would take an electron to flow from the switch to the light, it turns out to be (from memory) at least several minutes. So why does the light turn on straight away?
A rough picture is this: when you turn on the switch, you start pumping in electrons at one end of the circuit and extracting them from the other end. When an electron is pumped in, it repels other electrons that are already sitting in metal of the wire, which then bump other electrons. This process creates a rapid "wave" that passes along the wire so that almost immediately you put an electron in one end another one pops out the other end. And, almost immediately, the electrons that were in the light-bulb all along are set into motion, lighting the bulb.
EM field propagates at light speed? How
In the case of an electromagnetic wave, the electric and magnetic fields induce one another very rapidly as they change, creating a wave that propagates at the speed of light. This is shown by Maxwell's equations of electromagnetism.
If you're talking about electricity in a wire, then you need only worry about the electric field. Turning on the switch creates, almost immediately, an electrical potential gradient in the wire, which sets up a more-or-less constant electrical field through the wire. That doesn't quite happen at the speed of light, but it's near enough.
What's the source of the moving EM field?
All electric and magnetic fields are ultimately caused by electrically charged particles.
Let's look at a flash light, the voltage is 3 V, the electrons are moving in the wires at low speed, the light comes out instantly.
How em field propagate in the wire? Isn't the only thing that moves is electron in the wire? Is the electron carrying the em field?
The electrons move very slowly in your flash light. But what is important is not the electrons themselves but the energy they carry to the bulb.