Until you can give an actual unambiguous definition of what the "vp rest frame" is, yes. There are an infinite number of "vp rest frames". Which one are you talking about?
And it isn't the 4th time I've answered, but I have answered: one scenario at a time. Trying to tackle your rotating setup when we don't even have common ground on the scenario with a simple capacitor would be like trying to tackle calculus when we don't have agreement on simple arithmetic.