  We theoretically investigate the physical mechanism of the
screening-current-induced field (SCIF) in solenoid coils wound with
superconducting tape wires. We derive the direct relationship between the SCIF
and the magnetization of tape wires, and a scaling law for the SCIF and the
coil dimensions is demonstrated. A simple analytical expression of the SCIF is
obtained as functions of current load factor, tape wire width, and the coil
dimensions. We verify that the published data for the precise numerical
computation of SCIF are roughly fitted by our theoretical results for flat
coils where the height is smaller than the outer diameter.
