I'm curious about how to determine/calculate the charge on a parallel plate capacitor with unequal voltages applied to both sides. With a capacitor made of two plates with significantly different areas, from what I've read, you use the area of the plates that overlaps in the formula (along with the relative permittivity and the distance between the plates): (e*A)/d. This formula determines the mutual capacitance between the overlapping portion of the two plates, and the portion of the plates that doesn't overlap would have some self capacitance like charged sheets.
For a capacitor with voltage applied to one side, my understanding is that one plate will acquire some amount of charge because of self capacitance (it would act like an isolated conductor). What about the charge on a capacitor with unequal voltages at either plate/sheet (with plates/sheets of the same size)? Like if you had a 1000 volt capacitor connected to the positive of a 500 volt battery and the negative of a 100 volt battery to the other, so relative to ground, you had +250 volts at one end and -50 volts at the other (and you connected the other end of each battery to ground). Would the charge of each of the sides of the capacitor be the mutual capacitance times the voltage applied? But since voltage is a relative concept, would the voltage on each plate, and thus the charge be equal? Like would there effectively be 300 volts for both plates even though two unequal voltages were being applied (and so the charge could be unequal)? The concept confuses me and I'd appreciate some clarity.