An inhomogeneity into a conductive matrix deforms the flow pattern of an applied electric current. A usual current cloak can be defined as a permanent modification of the matrix properties around the inhomogeneity guaranteeing that the current flow pattern is similar before and after passing by the modified zone, so it implies the electrical invisibility of the inhomogeneous region. Here we introduce the concept of a current cloak that can be tuned --switched on and off, for example-- by means on an external field. We demonstrate analytically and using Finite Elements Simulations that a current cloak can be constructed and manipulated by an external magnetic field for a concrete system consisting in a magneto-resistive matrix with a stainless steel inclusion.
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