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It is shown that a previously unknown class of magnetization patterns exists in planar structures which have the unique property that all the flux escapes from one surface with none leaving the other side. A simple case is a constant amplitude rotating vector magnetization where the sense of rotation dictates which surface has no flux. More complicated magnetization patterns are elucidated. The likelihood that the one-sided flux phenomenon occurs partially in the normal write, the contact-printing and the print-through processes of tape recording is discussed. It is concluded that significant improvements in tape recording performance would ensue if means could be found to enhance the effect.