In the scenario you described, where the number of electrons in the anode increases while the number of electrons in the cathode stays the same, it does not necessarily imply an increase in voltage potential. The voltage potential between two points depends on the difference in electric potential energy per unit charge (voltage) between those points.
Voltage potential is typically created by a separation of charges, such as the accumulation of excess electrons on the cathode and a deficit of electrons on the anode. This charge separation creates an electric field that exerts a force on charged particles.
However, without a wire or a conducting path between the anode and cathode, there is no established circuit for the movement of electrons. In this case, the increased number of electrons in the anode would not directly affect the voltage potential between the anode and cathode.
To establish a voltage potential and create an electric current, a complete circuit is required. This circuit provides a closed path for electrons to flow from the anode to the cathode, facilitated by a conductive medium such as a wire. In such a circuit, the potential difference (voltage) between the anode and cathode can be established and measured.
Therefore, in the absence of a conducting path between the anode and cathode, the change in the number of electrons on the anode would not directly indicate an increase in voltage potential. The establishment of voltage potential requires a complete circuit for the flow of electric charges.