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A toroidal coil with N turns of wire has a square cross section of side a and an inner radius b. (a) Show that coil's self-inductance is given by L =(u_o)aN^2 *ln(a/b + 1)/2pi and calculate it in henries if a = 7.5 cm, b= 75 cm, N = 1200. (b) Determine the mutual inductance of a system consisting of the torodial coil from part a) and a long, straight wire running along the axis of symmetry of the coil. Assume the conductors closing the circuit are located far from the coil, so that their influence can be neglected. Find the ratio of the mutual inductance of the system to the self-inductance of the coil in the limit of large N. Explain.