How is electric field instantaneously generated inside a conductor connected across two terminals of a battery? I have learnt that the electric field that is responsible for current flow is generated inside a conductor as soon as the two ends of the conductor are connected or brought in contact with the two terminals of the battery. I have also learnt about the hydraulic analogy according to which the electric field is established across the conductor in the same way as hydrostatic pressure is transmitted across a fluid.
But I'm not convinced with this analogy neither can I see any mechanism by which the electric field is established across the conductor.
I reflected that the electric field may be established by some induction, i.e. maybe the electrons in the vicinity of the electrodes are drifted towards or away from the charged electrodes and this drift of charge carriers and the subsequent development of a non - zero charge in that region  induces the electrons in a farther region to respectively drift towards or away from the nearer electrode. Am I correct in my thinking? 
 A: First of all it is not instantaneous, all electric/magnetic  impulses are limited by the velocity of light.
On a simple picture, as you find the answers in the link confusing, concentrate on the neutrality of each molecule in the wire before an electric  field is imposed by the battery. There are electrons on the outside of the molecule and protons inside so the total field outside a molecule is for our purposes zero. A field from the battery terminal attracts an electron at a time delta(t) and imposes a velocity of attraction. Suddenly that molecule acquires an electric field, a positive one, which will pull an electron from an adjacent molecule and the electric field appears further down,  and so on down the line to the other terminal of the battery. This happens very fast, because even though the electron moves fairly slowly with a drift velocity, the signal travels fast and part of the signal is the electric field that appears much faster than the electron drift velocity. Think of a stadium wave where the wave moves but the people stay in place, happening very fast as far as electrons are concerned. 
This is a gross explanation, because in metals once a field starts the electrons move in bands not attached to individual atoms, thus have higher mobility than in non conductors, but that is a story you will learn if you study physics further.
A: The battery already has electric field around its poles. When you connect wires to  the battery, charges redistribute along the surface of the conductors in the circuit. These surface charges, including those on the battery, maintain the electric field inside the conductors and thus cause electric current.
