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A circular coil has a 12.5 cm radius and consists of 38.0 closely wound turns of wire. An externally produced magnetic field of magnitude 3.40 mT is perpendicular to the coil. (a) If no current is in the coil, what magnetic flux links its turns? (b) When the current in the coil is 3.31 A in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil?