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Magnetic-field propagation from a plasma to a probe through a partially ionized layer of low conductivity is studied. The model includes dispersive properties of the layer and a radiation condition in the probe wall dielectric. A mixed problem of initial and boundary conditions is solved by Laplace transform techniques. The results are applied to the discussion of magnetic probe reliability in plasma focus measurements. Attenuation of the magnetic field may be severe but the effect of finite diffusion time scales on the magnetic-field profile is negligible. Distortion of the signal may nevertheless arise due to changes of the attenuation with the time evolution of the layer.