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We report on cylindrical permanent-magnet structures that exploit the image effect in a surrounding circular soft-iron sheath. We present the theory for a general multipole ring, where the polarization direction α = (n + 1)ψ, n is a positive or negative integer, and ψ is the angular coordinate. For the uniformly magnetized case n = -1, a long cylindrical ring produces no field in its bore, and the field outside the cylinder is that of a linear dipole. When surrounded by the sheath, the field becomes uniform in the bore and zero outside the cylinder. Higher multipole fields can similarly be transformed from outward fields to inward fields by using the sheath. The field can be varied continuously by moving the sheath. We describe a small variable-field device using a Nd-Fe-B cylinder that produces a flux density of 0-400 mT.