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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?