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A simple sensor for magnetic flux leakage methods of detecting cracks on the surfaces of ferromagnetic pipes is proposed. We show that the crack position can be determined by the Fourier coefficients of the leakage magnetic flux density on a circle inside the pipe in the pipe cross-sectional plane. Coils that directly output the Fourier cosine and sine coefficients were made. The experimental results showed that, using only these two coils rather than dozens of magnetic sensors, the center position of a crack on the inside/outside surface of the pipe could be localized.