A researcher is conducting an experiment on electric potential, where he tries to make X number of electrons form a certain pattern. In the first pattern, these electrons are placed uniformly on a small ring with a circular electron arrangement pattern and the distance between the electrons is the same between one another. In the second pattern, similar to the first, only one electron is taken and placed in the middle of the ring. Calculate the minimum value of X so that this second pattern has less energy than the first pattern!

Please provide a step-by-step solution!