A measuring device for detecting a conductor that carries alternating voltage, includes a voltage source configured to produce two phase-shifted alternating voltages, two complex impedance elements having first connections, which are connected to the alternating voltages, and second connections, which are connected to each other and to which a differential voltage is applied, and a control device configured to control the alternating voltages in such a way that a component of the differential voltage synchronous with the alternating voltages is minimized in magnitude. The control device is configured to detect the conductor if a ratio of the alternating voltages does not correspond to a ratio of the complex impedance elements in the absence of the conductor. The second complex impedance element is changeable with a control voltage. A probe is configured to provide the control voltage as a function of an alternating electromagnetic field induced by the conductor.