Alternating current in a polyaniline film formed into a ring 8 mm in diameter was induced by an external alternating magnetic field under potentiostatic conditions of the film. Since the magnetically induced current flows without application of voltage, this technique allows us to evaluate the conductance without applying a voltage difference between two terminals on the film. The polyaniline ring was synthesized electrochemically on nine radially arrayed platinum rods of which the disk surfaces were exposed inward to the aniline solution. Polyaniline growing on the nine disks coalesced into a ring, leaving a small electrical gap. A given potential was applied to the ring through the nine disks until the steady state was attained. Two disks were connected to a current follower and the other seven were at open circuit. When the alternating magnetic field was applied to the potentiostated ring in sulfuric acid, the induced current was much larger in the conducting potential domain than that in the insulating domain, as for an ordinary a.c.-voltammogram of polyaniline-coated electrode. It was a linear function of the amplitude and the frequency of the magnetic field. It was analyzed using the theory of the mutual induction. There is no capacitive contribution because of the equipotential measurement. Variation of the current with the molar fraction of the conducting species, which was obtained from the absorption vs. potential curve, agreed with the variation of the conductance of random mixtures of glass beads and metal beads. The agreement supports the concept of the electric percolation at the electrochemical switching.