International audienceThis investigation addresses the following problem: (a) a binaryinhomogeneous dielectric (two distinct permittivities; those of thecore and of the mantle) object B is subjected to a quasistaticelectric potential P and the response F to this field is measured atvarious points outside the object. (b) Find the so-called ‘equivalent’permittivity ε of the homogeneous object H , having the same shapeand size as B , which gives rise to the same response F as B to thesolicitation P . This is treated as an inverse problem, in which F isthe simulated data and the parameter retrieval model is that of theinteraction of P with H . We show, for B a filled tube-like object, that:(1) this inverse problem can be solved for the retrieved value E of εin a mathematically-explicit form, (2) and E can provide consistent,meaningful, physical and geometric information as to the nature andproportion of the core and mantle components of the object, provideduncertainties concerning the measurement of F are small