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A single-layer flat-coil-oscillator activated by a low power backward tunnel diode has been elaborated and created. As an inductance in a pick-up circuit of the oscillator, such a flat coil served as a “magnetic-field” probe in such a measuring instrument. The created oscillator was activated both without and with an external capacitance C0 in its resonant circuit, i.e. the flat-coil oscillator might be also activated with its own (internal) capacitance Cc. Investigation of “probe-forma-tive” capabilities of this research instrument with such an unusual coil (versus C0) showed that with a reduction of the value of this capacitance the feeling (probing) field of such a probe exponentially becomes longer, i.e. these probes become more far-ranging with decreasing C0. The revealed property of “magnetic-field” probes would permit an essential widening of capabilities of flat-coil-based probe microscopes. It may also permit to enhance the efficiency of searching and detec-tion of the nodal structure, arising at an unusual phase transition from the “uni-form” to “non-uniform” superconductivity, predicted independently by Fulde and Ferrell, and Larkin and Ovchinnikov.