The invariance of the transport critical current value under variation of a sample cross-sectional shape

It is shown that, when an external magnetic field is absent, the value of transport critical current in high-temperature superconducting ceramics is a power function of the sample cross-sectional area and independent of the variation of the sample cross-sectional shape. This fact demonstrates that the distributions of critical current density and induced magnetic field in ceramics have an unusual nature, are functions of the sample cross-sectional shape, and enables the analytic description of the critical state in samples. The field and current distributions in the samples having round and square cross-sections are reported.