How electron movement produces current,instead of having a slow drift speed Just need a clarification here, how the current is produced due to the movement of electrons, in an external circuit,having a very slow drift speed.
Normally in a battery there is high potential terminal and low potential. Using these two terminals the external circuit is closed. Now within the battery the direction of the current flow and the electron flow is opposite to that of the external circuit. If I consider that positive current is flowing from the positive terminal to the negative terminal of the battery through the external circuit then we can say that positive terminal is at higher potential then the negative terminal of the battery. 
Now when we are closing the switch of an external circuit, in that case the electrons are moving from negative terminal to positive terminal of the battery, through the external circuit. But we also know that the drift speed is very slow, of the electron. But when we 
switch on some of the electrical devices, within a fraction of second the device starts working. If drift sped of electron is low, so how the device is working so fast ,(near about the speed of light,I guess), as we know that current flows due to the flow of the electrons.So how it is possible, in spite of electrons are having such a low drift speed ?
Please help me guys !!!!! 
 A: Am I correct that you can rephrase your question to 'electrons move so slow, how come that when I flip the light switch the light comes on basically instantly?'?
It's true that the electrons travel very slowly. But these electrons don't have to travel across the wire to power your light bulb.
In electromagnetism, we have the continuity equation $\nabla J = 0$. It says that current can't 'heap up' somewhere in the wire. So when you flip the switch, all electrons in the wire start moving simultaneously. 
It's analogous to a bicycle - when you start pedalling, the entire chain starts moving rather than the links closest to the pedals.
A: The information about beginning of the flow of current is transmitted through the propagation of electromagnetic waves and not with drift velocity of electrons. Hence, any electric appliance turns on almost instantly, when the switch is closed.
A: 
Although the electron velocity is very low, which is propagated almost instantaneously is the electric field. This causes the effect that all the electrons in the wire to start moving simultaneously (almost).
A: Electromagnetic force is not propagated by electrons, it is propagated by photons. By definition these travel at the speed of light (in the material). Impedance and capacitance play a part in how quickly the system responds to you turning it on / connection a battery, but are generally very small in a plain wire.
The electrons are moved by electromagnetism (in this case specifically by electrical potential difference), and the electromagnetic field is caused by the movement of electrons. The rate at which they move and are caused to move has nothing to do with the speed of propagation of the electromagnetic field that moves them.
You might as well say, "I was walking home at 4mph when I called my friend and invited him to meet me at my house. He drove there at 30mph. Given that we move at those speeds, how can the telephone message travel faster?". The analogy is not perfect since walking does not inherently cause phone calls, and the energy to move the vehicle didn't come via the phone call. The similarity is that the signal was caused (indirectly) by your movement home, and it caused your friend to move. Despite this causation the signal was not propagated by either of those motions, and neither was the energy.
A: This is to clarify Martin Petrei's answer. Electrons have an electric field and this field is already established between every electron in the conductor by field-to-field coupling. It is just like a long line of rail cars where their couplers are already compressed for pushing or are already in tension for pulling. You push or pull on one electron and this field-to-field coupling pushes or pulls every electron such that there is a near simultaneous action at the other end of the conductor. 
