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The deterministic prediction of both transient and CW field coupling to large complex electrical systems poses such a formidable problem that other approaches to predicting the coupling may be useful. The continuous wave coupling to a complicated electrical system is analyzed in terms of random small dipole interactions in the low-frequency limit (wavelengths > system components' sizes). Both random coupling to the incident wave and random interactions among the dipoles are considered. The variables being randomized are the incident direction and polarization, the sizes and orientations of the dipoles, the mutual coupling strengths, and the lumped load impedances. The resulting normalized current distributions are shown to be insensitive to the details of the model except at the extremely low and high percentiles. The magnetic dipole case is investigated in detail. Its resulting induced current distribution roughly resembles, but is not, a log-normal distribution with a standard deviation in the vicinity of -6 dB. This result provides insight into some recent measurements obtained for EMP transient field coupling to large systems. An important implication of the results is that for a variety of complicated systems, essentially consisting of many small elements that the coupling is dominated by low-frequency magnetic fields, the central parts of the induced current probability distributions are similar and nearly log-normal. However, conclusions based on the extrapolation of log-normality from measured values near the median to the extreme percentiles may be susceptible to sizeable errors.