A method and system according to which electrical communication is established between a primary circuit positioned inside a downhole tubular and a secondary circuit positioned outside the downhole tubular. In an exemplary embodiment, the method includes positioning the secondary circuit outside the downhole tubular, the secondary circuit including a magnetically permeable secondary core and a secondary winding extending proximate the secondary core; positioning a primary circuit inside the downhole tubular, the primary circuit including a magnetically permeable primary core and a primary winding extending proximate the primary core; and supplying electrical power and/or data to the primary winding with an electrical source so that a magnetic flux is channeled through the primary and secondary cores to induce an electromotive force in the secondary winding, thus establishing electrical communication between the primary and secondary circuits to transfer power and/or data therebetween.