In a certain experiment, we place two metal plates of area A parallel to each other and separated by a distance d to form a capacitor. The copper disks are mounted on nonconducting stands in a dry room which does not allow the conduction of charge through the air. The two plates are connected with wires to the opposite ends of a DC cell. We can increase the capacitance of such a setup by inserting a nonconductor, called a dielectric in electrical engineering parlance, between the plates. In this case, the capacitance of the device is Cdi = κCvac, where Cvac is the capacitance of the plates with a vacuum between them, κ is the dielectric constant of the nonconductor, and Cdi is the new capacitance.
In Experiment 1 we place two copper circular disks of area A1 a distance d1 apart, thus creating a capacitor with capacitance C1. We connect the two plates to opposite terminals of a battery which produces a potential ΔVbat. This produces a positive charge Q1 on one of the plates and an electric field E1 between the plates.
In Experiment 2 we reproduce the setup in Experiment 1. This time, however, the two disks are connected to the opposite ends of a battery which produces four times the potential as that in Experiment 1 (4ΔVbat).
In Experiment 3 we reproduce the setup in Experiment 1. Then the wires are removed from the copper plates. We place cellulose nitrate (a dielectric with dielectric constant k = 9) between the plates.
What is the magnitude of the potential difference between the plates at the end of Experiment 3?