  We design a device that generates fields canceling out a known probing field
inside a region to be cloaked while generating very small fields far away from
the device. The fields we consider satisfy the Laplace equation, but the
approach remains valid in the quasistatic regime in a homogeneous medium. We
start by relating the problem of designing an exterior cloak in the quasistatic
regime to the classic problem of approximating a harmonic function with
harmonic polynomials. An explicit polynomial solution to the problem was given
earlier in [Phys. Rev. Lett. 103 (2009), 073901]. Here we show convergence of
the device field to the field needed to perfectly cloak an object. The
convergence region limits the size of the cloaked region, and the size and
position of the device.
