Electricity and Return Current

Universal to the concept of electricity is the idea of a return current. No circuit can exist without the return. Electrons under pressure will tend to pop, one at a time, towards an area with less electron pressure or negative potential voltage. In this case the return current may not be a discrete electron returning to where the original kinetic electron left. Instead, a number of electrons will drift in to back-fill where the kinetic electron left.

The electrons will leave according to the probability mass function lambda to the k multiplied by e to the negative lambda divided by k factorial where lambda is the electron ejection rate. The Poisson distribution tells us that for a certain period of time and a certain surface area an average ejection rate will be described by the equation described above. 

The flux in the flow of electrons as energetic electrons move one way and then less energetic electrons back-fill in large numbers moving in the other direction show the capacitive charging of a dielectric medium. Electron kinetic energy begins to move both ways as the medium maximizes the energy stored in the kinetic electrons in the medium.