# Floating potential of a conductor in an electrical field

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I'm interested in the following general question: Assume x,y,z is an axes system, and that the y-z plane is occupied by a conductive plate at a known potential V with respect to the earth. Now, a conductive material M of neutral global electrical charge is placed at some distance of the plate, and is not connected to anything else. Furthermore, the distance of M to the plate is much smaller than the distance of M to anything connected to the earth (so that, the direct influence of the earth on M can be neglected). What is the potential of M with respect to the earth ?

For the sake of simplicity, it can be assumed that M is a copper cylindrical rod of length 1 along the x axis, located from x = 1 to x = 2. Regarding the unspecified parameters, any assumption can be done.
Also, if the "infinite plate" is problematic, it can be assumed it's a large disk or a large rectangular plate.