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.
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