Electric field between point and infinite plate

[Erikve]

Dear all,

I think I have an easy problem for you, however I get confused by the simplicity and complexity at the same time.

Situation is like this: I have a point charge at a distance d from an infinite plate with thickness comparable to the distance d. Is there difference between the electric field op these scenarios:

1. I put the infinite plate at ground and apply a voltage on the point charge
2. I put the point charge at ground and apply a voltage from the infinite plate

Naively my response: there is not difference. But when I thought about the distribution of charge carriers in both scenarios... the ground makes it complicated where charge is in both situations.

 

[Born2bwire]

You're always interested in the voltage/potential difference. In this case you seem to just be swapping the ground reference which can leave the voltage differences the same. The caveat being that the plate is conductive, thus making it an equipotential surface (otherwise one may argue that locally enforcing a potential on the plate does not make the entire plate the same potential).

Though I would point out that it does not make sense for you to make the point charge "ground." You still need to obey the basics of electrostatics which follows Poisson's equation. That is, the Laplacian of the potential is proportional to the charge density. But for a point charge, the potential field that satisfies this relationship is singular at the charge's location (Coulomb's Law). So if you took the position of the point charge as your ground reference then you would probably be introducing various singular potentials in inconvenient spots.