Clear the basic definition of current.
Current is the amount of flow of any entity through a cross-section in per unit time. Depending what the entity is, current can be - heat current, air current, charge current etc.
So here in case of electrodynamics-
The charge which is circulating has the magnitude 'q'.
As the path is a circle of radius 'r'. The total distance is 2TTr. The rate of flow of charge is 'v'.
We can conclude that the amount of charge flowing through a particular corss-section in a circle is
Or you can say that since i=q/t and t=2TTr/v. But the above method will aid you in arriving to the result in any situation.