The electromagnetic field response under the influence of an alternating magnetic field is investigated for an isometric ore body covered by a disseminated spherical zone. The embedding medium is homogeneous and a relatively poor electrical conductor. The formal solution of the diffraction problem is obtained when the overlying nonuniform conducting shell has a general spherical symmetry. More complete analysis is made for three important cases where the screening shell is assumed to have:1. a power law conductivity distribution,2. propagation constant decreasing linearly outside, and3. a homogeneous electrical behaviour.The computational procedure for the evaluation of the in-phase and quadrature components of the screening factor for the last case is presented along with some relevant curves for parametric values suitable in the exploration of massive sulfide deposits. The computed results establish a paradoxical phenomenon of negative screening, meaning that under favorable conditions an ore body with a conducting cover will show up better than an uncovered one. Though these results are contrary to the present philosophy of prospecting, they are able to explain some observations recorded in the field and model experiments. Because of the generalized treatment the analysis with suitable modifications can find applications in many other diffraction problems.