An easy quez on charge induction?

Suppose I have a negatively charged plate at -10000v (static) and a neutral plate in front of it; quiet close to it, this charged plate will induce +10000v in the inner surface of this neutral plate right??.or near to that potential difference if the case is not ideal isn’t it??.

And an opposite charge of the same magnitude in the outer surface of this neutral plate….that is -10000v right??

Just confirming….I don’t find things in such details in the net or the books…..I just thought bout……is this true??.this things been a real head ach to me

I doubt if any article has been written on this.

Answer:
Things are not exactly as you have described them.

The 'neutral' plate will exist at a potential that is somewhere between the positive & negatively charged surfaces.
While you don't specifically state that the neutral plate is a conductor of near-zero thickness, this is implied. As such, you would not measure a voltage differential across the 'neutral' plate. But, you could measure it's potential with respect to either the negative plate (-10 kV) or the reference positive surface.

We do this all the time in certain types of voltage sensors on high voltage electrical systems. Fundamentally, by placing a plate in the middle, you have created a capacitive voltage divider. These work for static as well as dynamic (AC or DC) electric fields. With careful selection of the materials and plate locations, it is possible to measure millions of volts with these dividers.

If your neutral plate is an insulator, then there will be charge accumulation on each side of the plate, as you have described. However, the voltages will depend on location and geometry of the various dielectric materials (insulators like air, vacuum, plastic, glass, etc.) involved.
The -10,000 V has to be in reference to something, in this case what you are calling neutral, so the voltage between the two plates will remain unchanged as you bring them closer together, but the charge distribution on the 2nd plate will be changed. Check this Wikipedia article for a visualization of this, if not an explanation.
There will be no separation of charges in the conductor, assuming it is close to ideal. For most practical purposes, you can assume there is no electric field inside a conductor. A conductor is an example of a faraday cage, except it isn't hollow. There is no electric field inside a faraday cage.

Unless you provide an electrical connection to the neutral plate, there will be no charge induced on it.

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