Electrostatics textbooks delight at computing the electric field or the potential created by a known distribution of charge, ignoring the fact that this is rather a non practical question. In practicality, you have a voltage generator and conductors. You know the output voltage of the generator with respect to the earth, and hence the electrical potential of the connected conductor. It turns out that I don't see, in my old books of physics, how to handle electrostatic questions related to the floating potential of conductors, even though they should be solvable somehow. To put flesh on bones, I propose 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.