A circular coil of wire, with N turns of radius a, is located in the field of an electromagnet. The magnetic field is perpendicular to the coil (that is, parallel to the axis of the coil) and its strength has the constant value B, over that area. The coil is connectd by a pari of twisted leads to an exteranl resistance. The toal resistance of this closed circuit, including that of the coil itself, is R. Suppose the electromagnet is turned off, its field dropping rapidly to zero. The induced electromotive force causes current to flow around the circuit. Derive a formula for the total charge Q = Sidt that passes through the resistor and explain why it does not depend on the rapidity with which the field drops to zero.