Abstract: Uniform magnetic field has many applications in scientific research and

engineering technology. Based on Biot-Savart law and the superposition principle of magnetic

field，the mathematical expressions of magnet- ic induction intensity created by four

parallel，coaxial and current-carrying square coils of equal size ( FPCSCS) are derived. By

using Taylor series expansion method，the conditions，under which the FPCSCS generates a mag-

netic field of the best uniformity，have been found. The uniformity of magnetic fields

produced by the FPCSCS in three cases is discussed. The results show that，in the optimum

situation，the FPCSCS can generate a very homoge- nous magnetic field with magnitude relative

deviation of less than 0.01% and direction deviation of less than 0.01 degree. Compared

with the homogenous magnetic fields of square Helmholtz coil，the magnetic field of FPCSCS has

obvious advantages，which are greater magnitude and better uniformity.

Key words: magnetic field homogeneity, square current-carrying coil, Helmholtz coil, Biot-Savart law