Charge Separation: Effects of Electric Field Intensity

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When a conductor is made to experience a field, there's a separation of kernels and electrons...now depending on the intensity of this fields, the degree of separation varies.

Now is this separation quantum?...I mean at one end there're absolutely no electrons, while in the other we have evenly distributed electrons.
 
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By kernels, I presume you mean the fixed positive charges in the conductor that do not move.. When the wire (conductor) is in an electric field (aligned along the E field), there is a very small displacement of the electrons in the conductor to produce a slight electric dipole moment of the conductor. The displacement of the electrons produces a counter electric field in the conductor such that there is no net electric field (voltage gradient) in the conductor. Since the electrons are primarily the conduction electrons which are free to move, the separation is not quantized. This is also true if the conductor is a dielectric, because the valence electrons are displaced.
 
No no...I'm not talking about a wire...consider a plate immersed in a field.