Solution for retarded vector potential due to a circular loop of current and perturbed by the presence of a permeable infinitely-long cylinder is derived from Maxwell's equations and the standard boundary conditions that the tangential component ofEis strictly continuous across the boundary, and the difference of the tangential components ofHon the boundary is equal to the true surface current. The geometry of the permeable core dictated the use of a circular cylindrical coordinate system for the problem. The dimensions of the current loop are assumed to be small, compared to the wavelengths of the field quantities involved, to justify the assumption of uniform current density throughout the loop. It has been shown that the resultant potential consists of two parts: one part is due to the loop only; and the other part is due to the presence of the permeable core. Using the expressions for the retarded vector potential, the Poynting vector and the rate of energy outflow have been calculated. The power outflow has been evaluated using a computer for certain sets of parameters. The method as to how similar procedure could be used to obtain solution for a prolate spheroidal core has been indicated.