please tell me, if a charged terminal is brought near a neutral grounded terminal, does the neutral grounded terminal acquire a equal and opposite charge or does it remain neutral?
ANSWER: Terminals are generally conductors. Conductors have zero electric field inside, in a static situation, so all field is cancelled out by a charge distribution on their surface that makes that field zero. So they have a charge on the surface and a net charge, yes. Usually equal and opposite.
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QUESTION: thank you, please tell me in a situation where there are two wires, one of the wires is only connected to earth, the second wire is connected to a 25kV DC power source. what will be the charge on the earthed wire end when it is brought over near the charged wire end. please see attached image.
ANSWER: I'm assuming that it's providing 25 kV relative to ground, which you didn't draw (there's no such thing as absolute potential, just relative potential) on the power supply. The amount of charge will be equal and opposite to the amount on the other wire, of course. However, the amount on that one terminal depends entirely on their relative geometry (from which you can compute their capacitance). Without knowledge of their geometry (closely spaced parallel plates, spheres of some radius, the distance of separation of the terminals, etc) I can't calculate that. If you have the capacitance, then C=Q/V (C=capacitance, V=25kV, and Q=charge).
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QUESTION: thank you, regarding "relative potential". so in the set up as in my NEW attached diagram, if the terminals were the same 25kV of "relative potential" But relative to ground one terminal was 25kv(-) and the other terminal was 50kV(-). both being negative relative to ground but with 25kV of "relative potential". this time the terminals are just sharp wire ends, close to each other.
so in this new set up (ignoring all the geometry) just dealing with the basics, would there be (+)positive ions produced on the 25kV (-)negative terminal wire? because it would change polarities?
The new sketch is still incorrect, but it doesn't matter. You have a 25 kV difference between "sharp wires." Still absolutely none of what I asked for. The precise geometry. How sharp? How far apart? The geometry is the only important thing for determining the stored charge. Sharp points and high voltage will create atmospheric ionization. The potentials you mention, since you didn't draw contacts between the high voltage supplies and ground, I will consider to be the only high voltages in this problem. Therefore, the higher potential wire will produce positive ions in this scenario. If you actually include ground and the surrounding environment, that answer may change.