In the context of image charges. Let say I have a very large grounded/earthed plate. If initially the total charge on the plate is 0 then we place a positive point charge, $Q$ just above its surface (at its centre). If the plate was not grounded/earthed then I know we would get a surface charge of $-Q$ on the top plane of the plate with the positive charge $Q$ distributed on the lower side of the plate so that the net charge on the plate remains $0$. But in the case of the grounded plate can we still say that the net charge on the plate is $0$? Or are charges allowed to move to and from ground?
My attempt at an answer: I don't think this is the case since grounding only defines the potential of the plate to be $0$. There is no closed circuit for electrons to flow to or from ground and therefore the net charge of the plate remains $0$.
Best Answer
There's more. An ideal ground can supply / absorb an arbitrary amount of charge while remaining at zero potential.
"A grounded conductor is a special type of equipotential: infinite amounts of electrical charge (± Q) can flow from / to ground to / from the conducting surface so as to maintain electrostatic potential V = 0 (Volts) at all times."
If your conducting plane is connected to an ideal ground, the plane can have zero potential and have net electric charge.
One doesn't need a closed path for electrons to flow except in the context of electric circuits. Electrons flow back and forth along, e.g., a long wire antenna and there is no closed path.
At any rate, for the problem of a large (effectively infinite) grounded conducting plane, if there is a charge $Q$ above the plane, there is net electric charge $-Q$ induced on the plane. See, for example, section 3.2.2 of Griffiths "Introduction to Electrodynamics", 4th edition.