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A uniqueness theorem for a static electric or magnetic field in an isotropic but saturable medium is presented. We show that if, in a given region, B and H are appropriately related and Maxwell's equations are satisfied, and if over the boundary of that region either normal B or tangential H is prescribed, then both B and H are unique in that region. A similar statement can be made about D and E in an electric field calculation if, in addition, we assume that the region is free of electric charge.
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Charles W. Steele (1973) studied this question.
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