Processes charging and discharging the charged conducting balls as a result of alignment of their potentials, and also charging balls from the same sources of a voltage are considered. The charges received by each balls are calculated. Thus the phenomenon of a mutual electric induction as a result of which in each of balls the infinite number of charges-images is formed is considered. Forces of interaction of balls of the different radiuses connected to same source of a voltage and having identical potentials are calculated. It is shown, that at removal of balls of various radiuses from each other force of their interaction passes through a local maximum. It is shown also, that the account of images only the first order in some cases is good enough approach. Results of experiments on measurement of force of interaction of balls which show the satisfactory consent with theoretical are resulted.