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For charged‐particle beam experiments, it is often necessary to measure the transverse position of a beam that is undergoing oscillations as it propagates axially in a conducting tube. This is usually done using small wire loops called B‐dot monitors which measure the change of magnetic flux. If the monitors are located at a radius R, which is of the same order as the wavelength of the beam oscillations, the B‐dot signal and the beam transverse position are related in a nonlocal manner. We consider this situation here and derive an integral equation relating the beam position to the B‐dot signals, for arbitrary displacement profiles, in the limit of small beam displacements. Solutions of this equation are obtained for special cases along with a numerical method for solving the general problem.