A rectangular core has fixed permeability μr >> 1, a square cross section of dimension a x a, and has centerline dimensions around its perimeter of b and d. Coils 1 and 2, having turn numbers N1 and N2, are wound on the core. Consider a selected core cross-sectional plane as lying within the xy plane, such that the surface is defined by 0 < x < a, 0< y< a. (a) With current I1 in coil 1, use Ampere's circular law to find the magnetic flux density as a function of position over the core cross-section. (b) Integrate your result of part (a) to determine the total magnetic flux within the core. (c) Find the self-inductance of coil 1. (d) Find the mutual inductance between coils 1 and 2.