In this thesis, we study the distributions of magnetic flux and current densities in a collection of very long, parallel coplanar superconducting strips with a desired number of strips. For the propose of the practical application, two specific strip configurations are of our interests. In the first configuration, the end of strips are so connected that the combined strips make of a superconducting closed loop and in the second, we will have an transmission-line arrangement. The external magnetic field is applied perpendicular to the plan of common plane of the strips and by making use of the so-called two dimensional complex field, we obtain the field distributions in a the superconducting systems with a several number of the strips and the slots. It is shown that in a system of 2n long strips with the equal widths, for even n, increasing the number of strips will increase the amount of flux passing through the central slot and the system will push the flux lines into the central hole. In configuration of transmission line, instead of applying an external magnetic field, the traort currents are passed through to the strips. In this case, again by using the concept of the two dimensional complex field, the magnetic field and current density profiles of the superconducting systems for several number of strips are studied in details. We will also investigating the superconducting systems for a several neighboring strips spacing and show that by changing the number of superconducting strips the so-called effective area will be changed and will be controlled as desired.
